Paper deep dive

A2TTA: Anchored-and-Agile Test-Time Adaptation for Evolving Traffic Sensor Networks

Du Yin, Xiachong Lin, Yue Tan, Jinliang Deng, Estrid He, Hao Xue, Flora D. Salim

Year: 2026Venue: arXiv preprintArea: cs.LGType: PreprintEmbeddings: 143

Intelligence

Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 93%

Last extracted: 8/3/2026, 1:54:55 AM

Summary

The paper introduces A2TTA, a framework for Test-Time Adaptation (TTA) designed for evolving traffic sensor networks. It addresses two main challenges: topology expansion (new sensors/connections) and temporal distribution shifts (long-term drift and short-term deviations). A2TTA freezes the forecasting backbone and uses an expandable node-conditioned FiLM calibrator. It separates adaptation into a persistent global state for long-term shifts and an agile local clone for transient, context-specific deviations, ensuring robust performance in continuously changing environments.

Entities (9)

A2TTA · methodframework · 98%EvoXXLTraffic · dataset · 95%Test-time adaptation · concept · 95%Temporal Distribution Shift · challenge · 93%Topology Expansion · challenge · 93%FiLM Calibrator · component · 92%Global Calibrator · component · 90%Local Clone · component · 90%TFNSW · dataset · 90%

Relation Signals (10)

A2TTA → addresses → Topology Expansion

confidence 95% · To handle Challenge 1, we attach an expandable and node-conditioned FiLM calibrator... to address Challenge 1

A2TTA → addresses → Temporal Distribution Shift

confidence 95% · To address Challenge 2, we maintain two complementary calibrator states... For persistent long-term shifts... for context-specific short-term deviations

A2TTA → evaluatedon → EvoXXLTraffic

confidence 95% · Extensive experiments on EvoXXLTraffic and TFNSW demonstrate consistent improvements

A2TTA → uses → FiLM Calibrator

confidence 92% · A2TTA couples two complementary designs... attach an expandable and node-conditioned FiLM calibrator

A2TTA → evaluatedon → TFNSW

confidence 90% · Extensive experiments on EvoXXLTraffic and TFNSW demonstrate consistent improvements

Global Calibrator → handles → Persistent Long-term Shifts

confidence 90% · For persistent long-term shifts, an anchored global calibrator is continually updated

Local Clone → handles → Transient Short-term Deviations

confidence 90% · For context-specific short-term deviations, an agile local clone is specialized

A2TTA → uses → Local Clone

Cypher Suggestions (0)

No Cypher suggestions yet.

Abstract

Abstract:Traffic forecasting is important for efficient traffic management and route planning in smart cities. Existing traffic forecasting studies typically assume fixed sensor graphs, overlooking the continuous evolution of real-world traffic networks, e.g., ongoing road network construction and evolving human mobility patterns. These dynamic changes can substantially degrade conventional forecasting models, motivating test-time adaptation (TTA) to efficiently adapt pretrained models during deployment. However, applying TTA to evolving traffic sensor networks remains challenging in two aspects. First, topology expansion introduces new sensors and connections, continuously reshaping the sensor graph. Second, tem- poral shifts vary in time scale and stability, requiring differentiated adaptation to long-term and short-term shifts. In this study, we address these challenges by proposing A2TTA, an Anchored-and-Agile Test-Time Adaptation framework for evolving traffic sensor networks, which transforms topology-induced forecasting errors into an expandable output calibration problem and separates tem- poral adaptation into persistent global correction and agile context-specific specialization. By jointly addressing topology evolution and multi-scale temporal shifts, A2TTA enables efficient and robust adaptation to continuously evolving traffic environments. Extensive experiments on ten real-world traffic networks demonstrate that A2TTA consistently improves forecasting performance across different backbones, datasets, and prediction horizons. Our code is available in this https URL.

PDF

Open source PDF →Open local PDF →

Trouble viewing inline? Open PDF directly →

Full Text

141,248 characters extracted from source content.

Expand or collapse full text

A 2 TTA: Anchored-and-Agile Test-Time Adaptation for Evolving Traffic Sensor Networks Du Yin du.yin@unsw.edu.au University of New South Wales Sydney, NSW, Australia Hong Kong University of Science and Technology (Guangzhou) China Xiachong Lin dawn.lin@student.unsw.edu.au University of New South Wales Sydney, NSW, Australia Yue Tan yue.tan@griffith.edu.au Griffith University Brisbane, Queensland, Australia Jinliang Deng dengjinliang@ust.hk Beihang University Beijing, China Estrid He estrid.he@rmit.edu.au RMIT University Melbourne, VIC, Australia Hao Xue haoxue@hkust-gz.edu.cn Hong Kong University of Science and Technology (Guangzhou) China Flora Salim flora.salim@unsw.edu.au University of New South Wales Sydney, NSW, Australia Abstract Traffic forecasting is important for efficient traffic management and route planning in smart cities. Existing traffic forecasting studies typically assume fixed sensor graphs, overlooking the continuous evolution of real-world traffic networks, e.g., ongoing road net- work construction and evolving human mobility patterns. These dynamic changes can substantially degrade conventional forecast- ing models, motivating test-time adaptation (TTA) to efficiently adapt pretrained models during deployment. However, applying TTA to evolving traffic sensor networks remains challenging in two aspects. First, topology expansion introduces new sensors and connections, continuously reshaping the sensor graph. Second, tem- poral shifts vary in time scale and stability, requiring differentiated adaptation to long-term and short-term shifts. In this study, we address these challenges by proposing A 2 TTA, an Anchored-and- Agile Test-Time Adaptation framework for evolving traffic sensor networks, which transforms topology-induced forecasting errors into an expandable output calibration problem and separates tem- poral adaptation into persistent global correction and agile context- specific specialization. By jointly addressing topology evolution and multi-scale temporal shifts, A 2 TTA enables efficient and robust adaptation to continuously evolving traffic environments. Exten- sive experiments on ten real-world traffic networks demonstrate that A 2 TTA consistently improves forecasting performance across Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. Conference’17, Washington, DC, USA © 2027 Copyright held by the owner/author(s). Publication rights licensed to ACM. different backbones, datasets, and prediction horizons. Our code is available in https://anonymous.4open.science/r/A2TTA. CCS Concepts • Information systems→ Sensor networks. Keywords Traffic Forecasting, Evolving Traffic Sensor, Test Time Adaptation ACM Reference Format: Du Yin, Xiachong Lin, Yue Tan, Jinliang Deng, Estrid He, Hao Xue, and Flora Salim. 2027. A 2 TTA: Anchored-and-Agile Test-Time Adaptation for Evolv- ing Traffic Sensor Networks. In . ACM, New York, NY, USA, 19 pages. 1 Introduction Traffic forecasting is vital for building smart cities and intelligent transportation systems, helping alleviate congestion and improve mobility by supporting efficient traffic management and route plan- ning [4,20,29,34,35]. Usually, existing traffic forecasting studies are built upon fixed sensor graphs, where nodes represent traffic sen- sors deployed at specific locations and edges characterize the spatial connectivity of road networks. To model complex spatio-temporal traffic dynamics and accurately predict future traffic states, e.g., traf- fic flow, speed, and demand, various data-driven methods have been developed, typically following a workflow of traffic data collection, graph construction, spatio-temporal modeling, and future-state prediction. This pipeline has substantially broadened the range of downstream applications that traffic forecasting can support, such as congestion management, route planning, and traffic control, etc. Traditional methods generally assume a static traffic network, fol- lowing a train-once-and-deploy paradigm where the trained model is expected to remain effective in a long period [9–11,21]. Unfortu- nately, this assumption rarely holds in practice, as real-world traffic arXiv:2607.25875v2 [cs.LG] 30 Jul 2026 Conference’17, July 2017, Washington, DC, USAYin et al. sensor networks continuously evolve over time. On the one hand, road networks undergo continuous construction and renewal, lead- ing to the deployment of new sensors and the removal of outdated ones. Meanwhile, ongoing urbanization reshapes road layouts and connectivity, further altering the underlying sensor graph. On the other hand, human mobility patterns also evolve over time due to changes in commuting behavior, population distribution, and transportation policies, resulting in shifts in traffic dynamics even when the road topology remains unchanged. In these cases, conven- tional train-once-and-deploy forecasting models may suffer from substantial performance degradation, as both the underlying sensor graph and traffic dynamics progressively shift away from those observed during training. To handle the above dynamic changes, a straightforward solution is to regularly train the model. However, retraining can be expensive and may overwrite useful knowledge with short-lived patterns. Under this circumstance, a promising so- lution is Test-Time Adaptation (TTA), which updates a pretrained model from data observed during deployment [8,26], rather than retraining the model from scratch. As a result, TTA maintains adap- tation efficiency while effectively reusing the knowledge encoded in the pretrained backbone. Despite the strong potential of TTA, existing vanilla TTA so- lutions fail to effectively handle the evolving traffic forecasting problem due to the following two challenges. One key challenge is Challenge 1 - Topology Expansion. Unlike conventional dis- tribution shifts that occur in a fixed input space, evolving traffic networks exhibit continuous expansion of both the node set and the graph structure. Specifically, the deployment of new sensors introduces previously unseen nodes and connections into the graph, which alters the local neighborhoods of existing nodes and reshapes local graph structures and spatial dependencies. It is hard for con- ventional TTA methods to deal with such topology-level shift since they are typically designed to adapt to shifts over a fixed set of nodes and a predefined graph topology, lacking the ability to cap- ture dynamic structural changes. In addition to topology expansion, evolving human mobility pat- terns over time introduce another key challenge, termed Challenge 2 - Temporal Distribution Shift. Due to periodic and irregular fluctuations in human behavior, the input-output relationships and spatio-temporal patterns encountered at test time can deviate from those learned during training. For example, long-lasting changes in population, road infrastructure, or transportation policies may in- duce long-term shifts to the overall traffic characteristics over years. In contrast, temporary events or unexpected incidents may cause short-term, context-specific shifts that are highly dependent on the specific temporal and environmental conditions. In Figure 1(a, b), we exhibit this evolving deployment setting and show the persis- tent drift and transient deviations alongside topology expansion, respectively. Also, labels become available for adaptation only after the forecasting horizon has elapsed. In this case, this challenge lies not only in adapting to temporal shifts, but in identifying distinct types of temporal shifts with varying time scales and degrees of sta- bility, and applying appropriate persistent corrections.adaptation strategies accordingly. To address the above challenges, we propose Anchored-and- Agile Test-Time Adaptation (A 2 TTA for short) for evolving traffic sensor networks. As illustrated in Figure 3, A 2 TTA couples two (a) Fixed Training Graph Frozen Forecaster Frozen Forecaster Expandable Node- conditioned FiLM (b) Evolving Deployment Persistent Drift Transient Deviation Topology Expansion Anchored Global Agile Local (c) A 2 TTA clone Labels released after H steps Predict onceDiscard Figure 1: Motivation and design overview of A 2 TTA. (a) The conventional fixed-graph assumption trains and deploys a forecaster on one unchanged sensor graph. (b) Deployment instead brings topology expansion together with persistent drift and transient deviations, while labels are released only after the forecasting horizon퐻. (c) A 2 TTA keeps the fore- casting backbone frozen, appends node embeddings to an expandable node-conditioned FiLM calibrator, and routes de- layed feedback to an anchored global state and a disposable local clone. complementary designs. To handle Challenge 1, we attach an ex- pandable and node-conditioned FiLM calibrator to the frozen back- bone, which corrects the base forecast by conditioning on recent node observations, temporal statistics, and an expandable node em- bedding. To address Challenge 2, we maintain two complementary calibrator states that operate at different temporal scales. For persis- tent long-term shifts, an anchored global calibrator is continually updated using all causally released samples retained in the feed- back pool and regularized toward its warm-up state. Meanwhile, for context-specific short-term deviations, an agile local clone is specialized using released samples weighted by temporal phase, traffic-pattern similarity, and recency. To prevent transient contexts from contaminating the persistent global state, the clone is used for a single prediction and then discarded. Through these comple- mentary designs, A 2 TTA enables topology-aware and temporally adaptive forecasting, providing an efficient and robust solution for forecasting in continuously evolving traffic sensor networks. Our main contributions are summarized as follows: •We formulate traffic forecasting on evolving sensor networks as a causal delayed-feedback adaptation problem, jointly considering topology expansion and multi-scale temporal distribution shifts. •We propose A 2 TTA, a lightweight and backbone-agnostic framework that converts node-heterogeneous forecasting errors into an expandable FiLM-based output calibration problem while keeping the forecasting backbone frozen. •We develop an anchored-and-agile adaptation mechanism that combines a persistent global calibrator for long-term drift with a disposable, context-specialized local clone for transient deviations. Extensive experiments on EvoXXLTraf- fic and TFNSW demonstrate consistent improvements across backbones, datasets, and forecasting horizons. A 2 TTA: Anchored-and-Agile Test-Time Adaptation for Evolving Traffic Sensor NetworksConference’17, July 2017, Washington, DC, USA Table 1: EvoXXLTraffic scale and sensor growth. DistrictSpan#Yr 푁 first →푁 last TimestepsObs.Size D032001–202525174→18592,611,8722.56B10.2 GB D042001–2025251266→41102,559,7446.63B26.5 GB D052005–2025216→5722,185,3440.50B2.0 GB D062005–20252113→7462,138,9760.84B3.4 GB D072001–2025253215→48882,629,72811.28B45.1 GB D082001–202525262→20742,612,7363.49B14.0 GB D102006–20252045→13962,051,7121.70B6.8 GB D111999–202527424→14402,788,1283.23B12.9 GB D122002–2025241783→25872,524,6085.73B22.9 GB Total1999–2025–22,102,848 35.97B 144 GB 2 Related Work Traffic forecasting has progressed from statistical time-series mod- els [1,27] to deep temporal and graph architectures. Representa- tive spatio-temporal graph neural networks (STGNNs) combine recurrent, convolutional, or diffusion operators with road-network structure [13,34,36], while later methods learn adaptive graphs or attention-based spatial dependencies [29,30,37]. Recent architec- tures such as STID and STAEFormer further improve forecasting efficiency and accuracy [15,20]. Although these methods can model complex and even adaptive spatial dependencies, they are gener- ally developed and evaluated under a fixed sensor universe. Our setting instead considers multi-year deployment in which sensors are added, graph topology changes, and traffic distributions drift simultaneously. Beyond fixed-graph forecasting, online and continual approaches address network evolution through replay, pattern memories, lo- calized updates, or expandable prompts [4,6,24,25]. Retrieval and test-time calibration methods further adapt predictions using his- torical patterns or streaming statistics [5,35]. However, existing approaches typically update substantial forecasting components, rely on explicit replay or pattern memories, or focus on tempo- ral drift over a fixed node set. A 2 TTA takes a different route: it freezes the forecasting backbone, introduces an expandable node- conditioned FiLM calibrator, and separates causal adaptation into a persistent global state and a disposable context-specialized local clone. Both states use only labels released after the complete fore- casting horizon has elapsed. A more complete review is provided in Appendix A.2. 3 Dataset and Empirical Motivation 3.1 EvoXXLTraffic Construction EvoXXLTraffic organizes five-minute records from the California Department of Transportation Performance Measurement System (PeMS) [3,33] into yearly graph snapshots for nine districts (D03– D08 and D10–D12). For each district and year, the union of observed sensors formsV 푦 , while persistent IDs align flow matrices and iden- tify sensor additions and removals. Missing values use sensor-wise forward fill, backward fill, and a zero fallback. Sensor coordinates define A 푦 through Haversine distances and a thresholded Gaussian kernel (휖= 0.1). TFNSW is a long-span external test network. District 03 (2001-2025, N=2354)District 04 (2001-2025, N=5112)District 05 (2005-2025, N=598) District 06 (2005-2025, N=950)District 07 (2001-2025, N=5309)District 08 (2001-2025, N=2931) District 10 (2006-2025, N=1580)District 11 (1999-2025, N=1966)District 12 (2002-2025, N=3212) 1999 2000 2005 2010 2015 2020 2025 Caltrans PeMS Sensor Deployment by District: First-Seen Year (Cohort) Figure 2: Sensor deployment across nine districts. 3.2 Sensor Network Growth Deployment cohorts in Figure 2 extend and densify road corridors, with sensor counts increasing by up to 95×. Table 1 gives the district- level scale. The structural diagnostics in Appendix A.1 show non- monotonic changes in average degree and graph density, motivating adaptation to both topology and traffic distributions. 4 Problem Formulation Following EvoXXLTraffic [33], we model each district as yearly graph snapshots whose sensor set, adjacency matrix, and traffic observations may change. 4.1 Evolving Sensor Graph For district푑and year푦, let X 푑 푦 , A 푑 푦 , andV 푑 푦 denote the traffic tensor, adjacency matrix, and active sensor set: D 푑 푒푣표 = n X 푑 푦 , A 푑 푦 ,V 푑 푦 o 푦 1 푦=푦 0 , X 푑 푦 ∈R 푇 푑 푦 ×푁 푑 푦 ×퐶 , 푁 푑 푦 =|V 푑 푦 |. (1) Here,푇 푑 푦 ,푁 푑 푦 , and퐶are the numbers of time steps, sensors, and channels. BothV 푑 푦 and A 푑 푦 may change between years. New sensors in year푦 are ΔV 푑 푦 =V 푑 푦 푑 푦−1 .(2) The intersection contains retained sensors, whileV 푑 푦−1 푑 푦 con- tains inactive ones. Sensors inΔV 푑 푦 appear in year푦’s training, validation, and test partitions but in no earlier snapshot. Thus, “new sensor” denotes a topology-expansion cohort rather than zero-label cold start. 4.2 Forecasting Task For clarity, we omit the district superscript푑below and focus on univariate traffic flow (퐶=1). Within yearly snapshot푦, let s 푡 ∈ R 푁 푦 denote the traffic state at time푡. The input and target windows are X 푡 =[s 푡−퐿+1 , . . ., s 푡 ] ∈R 푁 푦 ×퐿 , Y 푡 =[s 푡+1 , . . ., s 푡+퐻 ] ∈R 푁 푦 ×퐻 . (3) Conference’17, July 2017, Washington, DC, USAYin et al. For online batchB 푏 starting at window휏 푏 , target Y 푖 is available only if푖 + 퐻 ≤ 휏 푏 . The main evaluation uses|B 푏 |=1, so every prediction precedes the next test window. Yearly training and deployment lifecycle. For each year, the host method produces푓 휃 푦 from the chronological training partition and its standard validation procedure. The baseline and A 2 TTA share this checkpoint and seed. A 2 TTA freezes휃 푦 , expands and warms up the carried calibrator on the same training data, and updates only that calibrator during testing with released targets. The global calibrator is then carried to the next year and expanded for new nodes. 5 Methodology 5.1Overview: From Evolving-Graph Challenges to A 2 TTA Figure 3 illustrates A 2 TTA. Given the current graph snapshotG 푦 = (V 푦 , A 푦 )and input window X 푡 , a frozen backbone produces a base forecast. An expandable node-conditioned FiLM calibrator then corrects node- and horizon-specific bias without modifying the backbone. A delayed-feedback pool exposes each target only after its full forecasting horizon has elapsed. Released samples update a persistent global state for shared drift and a disposable local clone for the current context. The clone is used once and discarded, sepa- rating persistent from transient shifts without explicitly classifying them. 5.2 Expandable Node-Conditioned Calibration Frozen backbone interface. For a yearly graph snapshotG 푦 = (V 푦 ,A 푦 ) , let푓 휃 푦 be the matched year-specific checkpoint produced by the host forecasting method. It maps the current input window to an 퐻 -step base forecast: b Y base 푡 = 푓 휃 푦 (X 푡 , A 푦 ).(4) Once loaded by A 2 TTA,휃 푦 remains frozen during calibrator warm- up and online adaptation. The corresponding uncalibrated baseline uses the same checkpoint, so their difference isolates output cali- bration rather than backbone training. A 2 TTA consumes only the forecast and does not alter architecture-specific internal layers. Node-conditioned FiLM. For each window-node pair(푡,푛), we concatenate the base forecast standardized by exponential-moving statistics, the normalized input history, four temporal summaries (last value, mean, standard deviation, and slope), and a learnable node embedding: z 푡,푛 = ey base 푡,푛 ∥ x 푡,푛 ∥ Stat(x 푡,푛 )∥ e 푛 .(5) We use a shared two-layer multilayer perceptron (MLP). It maps z 푡,푛 to horizon-specific modulation vectors: [a 푡,푛 , b 푡,푛 ]=ℎ 휙 (z 푡,푛 ), 휸 푡,푛 = 1+ 1 2 tanh a 푡,푛 ,휷 푡,푛 = 휎 base b 푡,푛 .(6) The resulting FiLM calibrator produces by 푡,푛 =푔 휙 by base 푡,푛 , x 푡,푛 ,푛 =휸 푡,푛 ⊙ by base 푡,푛 +휷 푡,푛 .(7) Here,휎 base is the running standard deviation of the base forecasts. Zero initialization of the MLP output head gives휸 푡,푛 =1 and 휷 푡,푛 = 0, so the initial calibrator is the identity mapping. Expansion and warm-up. Asℎ 휙 is shared across nodes, its pa- rameterization is independent of the sensor-set cardinality. This property allows A 2 TTA to accommodate topology growth without altering the shared correction function: when new sensors enter snapshot푦. Only their embedding rows are added while existing em- beddings and shared FiLM parameters are preserved. The matched backbone encodes the current topology through A 푦 and remains frozen, whereas the global calibrator inherited from year푦−1 pre- serves adaptation knowledge across graph snapshots. Before online deployment in year푦, the expanded calibrator is warm-started on the chronological training partition. The validation MAE is gener- ated without gradient updates, and test targets remain inaccessible at this stage. The resulting state휙 푦,0 combines inherited calibration knowledge and serves as the proximal reference for subsequent updates, which use only causally released test labels. 5.3 Causal Delayed-Feedback Pool A forecast at chronological index푖covers푖+1:푖+퐻, so its complete target Y 푖 becomes available at푖 + 퐻. After prediction, the corre- sponding record enters a pending queueQ. At the start of batch푏, whose first index is휏 푏 , records satisfying푖+ 퐻 ≤ 휏 푏 are released into a bounded first-in, first-out (FIFO) pool: P 푏 = Tail 푀 ( P 푏−1 ∪ R 푖 ∈ Q | 푖+ 퐻 ≤ 휏 푏 ) ,(8) where푀is the pool capacity. EachR 푖 stores the input window, cached base forecast, observed target, node indices, and chronologi- cal index. Released records leaveQ. Both adaptation branches read onlyP 푏 , so pending targets cannot leak into adaptation. 5.4 Anchored Global Adaptation The persistent global state is updated from every released record retained inP 푏 once the pool is sufficiently populated: L g (휙 ;P 푏 )= 1 |P 푏 |푁 푦 퐻 ∑︁ 푖∈P 푏 ∑︁ 푛∈V 푦 퐻 ∑︁ ℎ=1 b푦 휙 푖,푛,ℎ −푦 푖,푛,ℎ + 휆 c L con + 휆 p ∥휙 −휙 푦,0 ∥ 2 2 ,(9) where b Y 휙 푖 =푔 휙 ( b Y base 푖 ,X 푖 ), andL con is the mean absolute difference between predictions under two weak perturbations of the same input. Starting from휙 g 푏−1 , we take퐾 g AdamW steps on eq. (9) to obtain휙 g 푏 . The full-pool term favors patterns shared across contexts, while the proximal term limits departure from휙 푦,0 . This reduces persistent overreaction to transient samples. The updated state is retained across batches and carried to the next yearly graph snapshot. 5.5 Agile Local Specialization The persistent state may underfit a short-lived traffic regime. Before predicting batch푏, A 2 TTA creates a disposable local state휙 l 푏 ← copy(휙 g 푏 ) and updates only this clone. Online evaluation processes one chronological window at a time, so|B 푏 |=1; we retain batch A 2 TTA: Anchored-and-Agile Test-Time Adaptation for Evolving Traffic Sensor NetworksConference’17, July 2017, Washington, DC, USA Nᵧ sensors Node Embedding lastmeanstdslope Frozen Backbone Base Forecast Current Input Labels Unavailable Labels Available Wait H Steps t-M-H+1 Enqueue Released pool Current Batch Context Persistent t Anchored Global Adaptation t-H Current window Current Prediction FIFO Ephemeral Discard After Prediction Calibrated Forecast high low ... Released Pool Pending Queue Historical Context Temporal Statistics concat Node-conditioned FiLM Calibrator t-H+1 ... clone Agile Local Specialization Warm-up Initialisation (anchor reference) Global Update Context Weighting max capacity M=512 Context-weighted Samples Sensor Readings Road-network Graph Sensor Past Local Update Local Clone Captures long-term drift from released history causal / leakage-free phase · pattern similarity · recency Figure 3: Overview of A 2 TTA. An expandable node-conditioned FiLM calibrator corrects heterogeneous forecast bias as the graph expands. A pending and released feedback pipeline enforces causal label access. A persistent global state and a disposable local clone handle long-term and context-specific temporal shifts, respectively. notation for generality. Each released window 푖 is summarized by q 푖 = mean 푛 x 푖,푛 ∥ mean 푛 by base 푖,푛 , q 푏 = mean 푠∈B 푏 ,푛 x 푠,푛 ∥ mean 푠∈B 푏 ,푛 by base 푠,푛 .(10) Its relevance to the current batch combines temporal phase, pattern similarity, and recency: 휋 푖,푏 = 푒 −푑 tod (푖,푏)/휔 tod ( 0.7+ 0.3 1[dow 푖 = dow 푏 ] ) , 휅 푖,푏 = max 0, cos(q 푖 , q 푏 ) + 10 −3 , 휌 푖 = 0.5+ 0.5푟 푖 , 푎 푖,푏 = 휋 푖,푏 휅 푖,푏 휌 푖 , e푤 푖,푏 =|P 푏 | softmax 푖∈P 푏 log(max푎 푖,푏 ,휖) 휏 , ̄ 푤 푖,푏 = clip e푤 푖,푏 ,푐 −1 ,푐 , 푤 푖,푏 = ̄ 푤 푖,푏 1 |P 푏 | ∑︁ 푗∈P 푏 ̄ 푤 푗,푏 , 푖 ∈ P 푏 . (11) where푑 tod is the circular time-of-day distance and푆 day is the number of sampling steps per day. We set 휔 tod = max(푆 day /12, 1).(12) Thus,휔 tod =24 for five-minute PEMS data and 2 for hourly TFNSW data. The term푟 푖 ∈ [0,1]is normalized recency within the pool. The day-of-week indicator rewards phase agreement. We use휖=10 −6 , temperature휏=1, and clipping constant푐=5. The clipped weights are rescaled to have unit mean. Their effective sample size is ESS(w 푏 )= Í 푖∈P 푏 푤 푖,푏 2 Í 푖∈P 푏 푤 2 푖,푏 .(13) IfESS(w 푏 )<0.2|P 푏 |, we use uniform weights,푤 푖,푏 =1. The same window weight is applied to every node in record푖. The local clone then minimizes L l (휙 l 푏 ;P 푏 )= 1 |P 푏 |푁 푦 퐻 ∑︁ 푖∈P 푏 ∑︁ 푛∈V 푦 푤 푖,푏 by l 푖,푛 − y 푖,푛 1 ,(14) Conference’17, July 2017, Washington, DC, USAYin et al. Algorithm 1 Causal adaptation with global and local states in A 2 TTA Require:Frozen푓 휃 푦 , warm-started푔 휙 푦,0 , streamB 푏 , delay퐻, capacity푀, global- update intervalΔ, minimum pool size푚= max8,⌊0.1푀⌋ Ensure: Causal forecasts b Y 푏 1: Q ← ∅; P ← ∅; 휙 g ← 휙 푦,0 2: for each batch B 푏 = (X 푏 , A 푦 ) starting at index휏 푏 do 3:Move all records with푖+퐻 ≤ 휏 푏 from Q to P; retain the latest 푀 4: if |P| ≥ 푚 and휏 푏 modΔ= 0 then 5:for푘= 1,...,퐾 g do 6:휙 g ← AdamW 휙 g ,∇ 휙 g L g using all of P 7:end for 8: end if 9: b Y base 푏 ← 푓 휃 푦 (X 푏 , A 푦 ) 10: if |P| ≥ 푚 then 11:휙 l 푏 ← copy(휙 g ) ; compute푤 푖,푏 푖∈P by eq. (11) 12:for푘= 1,...,퐾 l do 13:휙 l 푏 ← AdamW 휙 l 푏 ,∇ 휙 l 푏 L l 14:end for 15: b Y 푏 ← 푔 휙 l 푏 ( b Y base 푏 , X 푏 ) ; discard 휙 l 푏 16: else 17: b Y 푏 ← 푔 휙 g ( b Y base 푏 , X 푏 ) 18: end if 19:Emit b Y 푏 and enqueue each current window푖 in Q with release time푖+퐻 20: end for After 퐾 l AdamW steps, the clone predicts the current batch: b Y 푏 =푔 휙 l 푏 ( b Y base 푏 , X 푏 ).(15) The clone is discarded after use, so local changes do not enter the next batch. Before the released pool is sufficiently populated, A 2 TTA predicts directly with the global state. 5.6 Unified Online Procedure Algorithm 1 summarizes the causal order. Eligible labels are re- leased before adaptation, the global state is updated before the local clone is created, and current windows are enqueued only after their forecasts are emitted. 6 Experiments 6.1 Experimental Settings Each year uses a chronological 60%/20%/20% train/validation/test split. PEMS windows contain 12 five-minute steps and TFNSW windows contain 12 hourly steps. All methods share the graph snapshots, splits, test windows, and metric code. Normalization uses training statistics only; validation and test targets do not enter preprocessing. Online methods process one chronological window at a time, match nodes by metadata sensor IDs, and release each target af- ter 12 steps. A 2 TTA keeps 512 released windows and updates its global state every 64 windows. Static methods receive the same windows without test labels. We report cumulative mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE) at horizons 3, 6, and 12. Avg averages the cumulative scores from horizons 1 to 12, with Avg-MAE as the pri- mary metric. Results use five paired seeds unless noted otherwise. A 2 TTA(OLAN) and A 2 TTA(STAE) load and freeze the exact per- year Online-AN and STAEFormer checkpoints, respectively. Other than learning rate, their adaptation settings are shared. Appen- dix A.7 lists the learning rates and sensitivity results. 6.2 Baselines We compare nine static forecasters (DCRNN, ASTGNN, TGCN, GWN, STID, STNorm, iTrans, DLinear, and STAEFormer); Pretrain, Retrain, Online-N, and Online-AN; four evolving-graph methods (TrafficStream, PECPM, STKEC, and EAC); STRAP and ST-TTC; and zero-shot (ZS) or yearly fine-tuned (FT) versions of Chronos-2, TimesFM 2.5, and Moirai-2.0. Each matched A 2 TTA/backbone pair shares checkpoint seeds, yearly cohorts, and preprocessing. New-sensor results use the meta- data set differenceV 푦 푦−1 at every graph-growing transition with the same five paired seeds. This isolates calibration from check- point, cohort, and node-order differences. 6.3 Main Results Overall performance. Results for three representative networks appear in Table 2. A 2 TTA(STAE) has the lowest MAE, RMSE, and MAPE on all three, reducing Avg-MAE over frozen STAEFormer by 9.4%, 13.8%, and 29.4%. On TFNSW, A 2 TTA(OLAN) reduces MAE from 130.61 to 86.78 (33.6%) and RMSE from 235.35 to 176.97 (24.8%). Comparison with time-series foundation models. TSFMs are ref- erence rows and are not included in the non-foundation ranking. A 2 TTA(STAE) outperforms every zero-shot and fine-tuned TSFM cell in Table 2, while updating only its calibrator after label release. Appendix A reports the other seven PEMS districts and horizons 3, 6, and 12 for all ten networks (tables 3 to 6). Forecast horizons. Across all 12 steps in Figure 4, A 2 TTA(STAE) has the lowest error on PEMS03 and TFNSW. Its mean per-step MAE reductions over frozen STAEFormer are 8.2% and 27.3%. Appendix A gives results for all sensors and the newly added subset on all ten datasets (figs. 12 and 13). 123456789101112 Horizon 10 20 MAE MAE 123456789101112 Horizon 100 200 MAE 123456789101112 Horizon 20 40 RMSE RMSE 123456789101112 Horizon 200 400 RMSE 123456789101112 Horizon 20 40 MAPE (%) MAPE (%) 123456789101112 Horizon 100 200 MAPE (%) (a) PEMS03(b) TFNSW A2TTA(STAE)STAEFormerST-TTCEACGWNSTNorm Figure 4: All-sensor per-step errors on PEMS03 and TFNSW. Lower is better. A 2 TTA: Anchored-and-Agile Test-Time Adaptation for Evolving Traffic Sensor NetworksConference’17, July 2017, Washington, DC, USA Table 2: Average results on PEMS03, PEMS04, and TFNSW (part 1 of 3). Each row is one baseline, with MAE, RMSE, and MAPE reported for each dataset. Avg is the mean cumulative-horizon score over prediction lengths from 1 to 12. Chronos-2 uses multivariate graph-grouped inference, and its fine-tuned variant uses per-year low-rank adaptation (LoRA). Values are mean± standard deviation when available; deterministic zero-shot runs are shown as±0.00. MAPE is in percent. Bold and underlining mark the best and second-best non-foundation methods; foundation-model rows are not ranked. CategoryBaseline PEMS03PEMS04TFNSW MAERMSE MAPE (%)MAERMSE MAPE (%)MAERMSE MAPE (%) Static STGNN Backbones DCRNN14.99 ±0.18 24.90 ±0.19 28.69 ±0.86 22.22 ±0.27 34.58 ±0.32 20.53 ±0.40 179.87 ±14.50 303.16 ±19.20 211.72 ±42.72 ASTGNN15.15 ±0.10 25.15 ±0.17 26.56 ±0.43 22.45 ±0.09 34.96 ±0.12 19.29 ±0.42 140.15 ±0.82 247.22 ±1.02 125.28 ±3.02 TGCN 15.88 ±0.10 30.12 ±0.40 28.95 ±0.89 23.60 ±0.37 38.82 ±0.55 20.15 ±0.28 208.33 ±1.48 390.75 ±3.25 177.95 ±3.89 GWN15.33 ±0.26 25.15 ±0.39 28.01 ±0.71 23.41 ±0.27 35.69 ±0.22 19.94 ±0.55 170.89 ±3.29 313.61 ±5.86 138.49 ±10.57 Naïve Schemes Pretrain31.37 ±1.11 41.64 ±0.99 50.04 ±2.80 153.33 ±6.62 186.37 ±7.58 82.25 ±2.99 262.63 ±10.87 383.38 ±12.29 430.83 ±35.95 Retrain14.16 ±0.15 23.46 ±0.14 26.29 ±0.58 21.64 ±0.20 33.58 ±0.22 19.15 ±0.30 138.04 ±0.62 247.58 ±1.00 104.00 ±3.59 Online-N17.47 ±0.16 28.29 ±0.08 29.62 ±1.04 38.46 ±0.27 51.85 ±0.46 26.93 ±0.71 174.36 ±3.31 318.17 ±5.87 129.82 ±8.24 Online-AN 13.80 ±0.05 22.89 ±0.11 24.96 ±0.21 21.01 ±0.26 32.73 ±0.31 17.82 ±0.31 130.61 ±0.96 235.35 ±1.95 99.93 ±3.54 Evolving Graph TrafficStream14.32 ±0.20 23.60 ±0.28 27.63 ±1.67 21.43 ±0.53 33.35 ±0.60 18.83 ±0.59 145.42 ±2.41 259.40 ±4.67 106.92 ±8.01 PECPM 14.90 ±0.81 24.32 ±0.98 27.78 ±2.30 25.16 ±3.18 39.17 ±4.12 22.29 ±3.69 174.19 ±22.07 318.61 ±45.67 106.24 ±4.44 STKEC14.47 ±0.22 23.89 ±0.34 27.58 ±0.64 22.78 ±1.14 34.78 ±1.18 21.54 ±1.53 147.86 ±1.05 259.82 ±2.21 148.01 ±7.69 EAC15.91 ±0.48 26.40 ±0.88 30.12 ±0.81 34.02 ±9.03 48.20 ±9.87 39.19 ±17.54 137.90 ±1.42 245.35 ±1.93 119.37 ±14.85 Retrieval TTC STRAP14.15 ±0.13 23.37 ±0.22 26.12 ±0.31 21.93 ±0.67 33.78 ±0.64 19.49 ±0.57 135.57 ±1.80 243.47 ±4.15 104.21 ±3.09 ST-TTC13.98 ±0.14 23.18 ±0.13 26.15 ±0.57 21.33 ±0.20 33.21 ±0.22 19.04 ±0.29 144.41 ±0.72 257.96 ±1.08 106.33 ±3.01 Static Forecasting Backbones STID 15.14 ±0.14 27.10 ±0.38 26.44 ±0.62 22.43 ±0.18 35.63 ±0.31 18.51 ±0.26 153.63 ±6.20 307.19 ±10.11 112.25 ±11.68 STNorm 18.20 ±0.47 28.58 ±0.65 52.94 ±2.57 23.99 ±0.62 36.65 ±0.80 27.98 ±1.51 148.78 ±2.33 275.25 ±3.16 182.00 ±6.10 iTrans14.21 ±0.13 23.42 ±0.14 26.79 ±0.71 21.22 ±0.11 33.04 ±0.17 19.36 ±0.25 144.04 ±0.82 257.27 ±2.16 113.97 ±6.78 DLinear 15.73 ±0.06 26.23 ±0.04 28.55 ±0.98 23.58 ±0.18 36.54 ±0.22 19.60 ±0.33 182.20 ±1.03 318.13 ±1.10 187.17 ±5.55 STAEFormer12.26 ±0.11 20.58 ±0.12 23.06 ±0.64 19.38 ±0.94 30.64 ±1.20 16.97 ±0.95 96.12 ±1.67 190.33 ±2.83 66.43 ±2.35 Times-series Forecasting Foundation Model Chronos-2 (ZS)15.27 ±0.00 26.98 ±0.00 25.83 ±0.00 21.58 ±0.00 35.22 ±0.00 17.62 ±0.00 227.74 ±0.00 440.18 ±0.00 120.67 ±0.00 Chronos-2 (FT)13.31 ±0.01 23.66 ±0.03 22.80 ±0.03 18.94 ±0.04 31.89 ±0.12 15.25 ±0.01 160.20 ±0.68 323.47 ±2.06 78.26 ±0.28 TimesFM2.5 (ZS) 15.91 ±0.00 27.86 ±0.00 26.71 ±0.00 23.49 ±0.00 37.69 ±0.00 19.32 ±0.00 266.77 ±0.00 487.06 ±0.00 160.45 ±0.00 TimesFM2.5 (FT) 14.16 ±0.01 25.36 ±0.04 23.79 ±0.01 20.92 ±0.02 35.20 ±0.02 16.65 ±0.02 215.22 ±0.33 420.65 ±0.52 124.25 ±0.83 Moirai-2.0 (ZS) 16.19 ±0.00 28.00 ±0.00 26.15 ±0.00 24.52 ±0.00 38.87 ±0.00 19.11 ±0.00 294.05 ±0.00 545.09 ±0.00 137.97 ±0.00 Moirai-2.0 (FT) 13.95 ±0.01 24.51 ±0.03 24.18 ±0.01 20.68 ±0.03 34.42 ±0.09 16.78 ±0.02 142.36 ±0.28 303.78 ±0.69 62.69 ±0.22 Ours A2TTA(STAE)11.10 ±0.04 18.87 ±0.07 21.46 ±0.18 16.70 ±0.11 27.46 ±0.15 14.89 ±0.05 67.89 ±0.32 147.15 ±0.64 54.66 ±0.33 A2TTA(OLAN) 12.19 ±0.04 20.72 ±0.07 23.43 ±0.27 18.15 ±0.05 29.59 ±0.07 16.41 ±0.28 86.78 ±0.24 176.97 ±0.84 66.01 ±1.49 6.4 Delayed-Label Sensitivity Figure 5 uses all ten networks. For PEMS12, Avg-MAE rises by 0.68% at 524 steps, 0.95% at 1,036 steps, and 0.65% without online labels. Across ten networks, the median increases at 524 steps are 0.62% for A 2 TTA(OLAN) and 0.63% for A 2 TTA(STAE); without online labels, they are 0.44% and 0.80%. The sweep changes only the release delay under the one-window protocol. 6.5 Ablation Study Full A 2 TTA has the lowest Avg-MAE in seven of eight settings in Figure 6. On Online-AN and STAEFormer, respectively, reverting to the frozen backbone raises error by 6.5% and 6.7%, replacing FiLM with a static affine transform by 3.7% and 4.7%, and removing the local clone by 1.2% and 1.6%. Freezing FiLM after warm-up is worse in seven settings but better on STAEFormer with PEMS06. Appendix A.8 defines the variants and gives the full results. Default 12 steps 76 steps 140 steps 268 steps 524 steps 1,036 steps No labels Total label-release latency (forecast steps) 0.0 0.2 0.4 0.6 0.8 1.0 Avg-MAE increase vs default (%) A2TTA (OL-AN)A2TTA (STAEformer) Figure 5: Delayed-label sensitivity; bands show the interquar- tile range. 6.6 Newly Added Sensors / High-Drift Periods For the metadata-defined new-sensor cohort, A 2 TTA(STAE) is best in five of six panels in Figure 7: all metrics on PEMS07 and MAE and MAPE on TFNSW. A 2 TTA(OLAN) has lower TFNSW RMSE (177.20 versus 178.38). A 2 TTA(STAE) reduces MAE over frozen Conference’17, July 2017, Washington, DC, USAYin et al. 12.513.0 Avg-MAE Full A2TTA w/o local clone FiLM → affine w/o online TTA backbone only A2TTA(OL-AN) PEMS03 1819 Avg-MAE PEMS04 10.511.0 Avg-MAE PEMS05 1314 Avg-MAE PEMS06 11.011.5 Avg-MAE Full A2TTA w/o local clone FiLM → affine w/o online TTA backbone only A2TTA(STAE) 171819 Avg-MAE 9.509.7510.00 Avg-MAE 111213 Avg-MAE Figure 6: Component knockouts on four PEMS datasets and two frozen backbones. DCRNN ASTGNN TGCN GWN Pretrain Retrain OL-N OL-AN TrafStm PECPM STKEC EAC STRAP ST-TTC STID STNorm iTrans DLinear STAEFormer Chronos2-FT-M† TimesFM-FT† Moirai2-FT† A2TTA(OL-AN) A2TTA(STAE) 0 5 10 15 20 25 30 35 MAE PEMS07 18.3 17.4 22.0 18.2 40.9↑ 16.2 15.4 15.6 15.3 16.5 15.5 16.4 48.5↑ 16.2 17.0 23.2 16.5 17.4 14.0 16.6 17.9 17.5 14.3 12.8 DCRNN ASTGNN TGCN GWN Pretrain Retrain OL-N OL-AN TrafStm PECPM STKEC EAC STRAP ST-TTC STID STNorm iTrans DLinear STAEFormer Chronos2-FT-M† TimesFM-FT† Moirai2-FT† A2TTA(OL-AN) A2TTA(STAE) 0 50 100 150 200 250 300 TFNSW 166.4 137.4 194.2 185.3 258.8 135.3 168.3 128.0 143.0 167.6 145.7 166.0 222.1 135.3 167.5 215.9 140.6 174.5 125.4 160.2 215.2 142.4 87.8 83.2 DCRNN ASTGNN TGCN GWN Pretrain Retrain OL-N OL-AN TrafStm PECPM STKEC EAC STRAP ST-TTC STID STNorm iTrans DLinear STAEFormer Chronos2-FT-M† TimesFM-FT† Moirai2-FT† A2TTA(OL-AN) A2TTA(STAE) 0 10 20 30 40 50 60 70 80 RMSE 30.9 29.0 42.2 29.8 52.7 26.9 25.8 26.1 25.7 26.9 26.0 26.8 71.6↑ 26.9 28.4 36.9 27.3 29.6 24.4 31.1 33.6 32.4 24.6 22.4 DCRNN ASTGNN TGCN GWN Pretrain Retrain OL-N OL-AN TrafStm PECPM STKEC EAC STRAP ST-TTC STID STNorm iTrans DLinear STAEFormer Chronos2-FT-M† TimesFM-FT† Moirai2-FT† A2TTA(OL-AN) A2TTA(STAE) 0 100 200 300 400 500 600 277.3 239.3 356.0 336.0 372.5 240.1 297.4 228.7 251.9 302.5 252.4 301.1 354.6 240.1 330.4 388.7 249.4 302.5 247.3 323.5 420.6 303.8 177.2 178.4 DCRNN ASTGNN TGCN GWN Pretrain Retrain OL-N OL-AN TrafStm PECPM STKEC EAC STRAP ST-TTC STID STNorm iTrans DLinear STAEFormer Chronos2-FT-M† TimesFM-FT† Moirai2-FT† A2TTA(OL-AN) A2TTA(STAE) 0 10 20 30 40 50 60 MAPE (%) 22.3 20.6 22.9 21.7 41.0 20.2 21.4 19.2 19.0 22.5 19.1 22.4 60.9↑ 20.2 25.4 43.0 20.9 20.2 17.6 20.0 21.2 21.2 17.5 16.1 DCRNN ASTGNN TGCN GWN Pretrain Retrain OL-N OL-AN TrafStm PECPM STKEC EAC STRAP ST-TTC STID STNorm iTrans DLinear STAEFormer Chronos2-FT-M† TimesFM-FT† Moirai2-FT† A2TTA(OL-AN) A2TTA(STAE) 0 50 100 150 200 250 193.5 129.3 168.7 150.2 388.1↑ 107.3 130.0 101.7 105.0 106.1 143.6 121.3 241.0↑ 107.3 107.2 332.7↑ 113.9 182.9 74.3 78.3 124.2 62.7 68.1 61.8 † TSFM-FT: all-sensor Avg reference (layout preview only); all other bars: new-sensor Avg. Static STGNN Naïve Evolving Continual Retrieval / TTC Other Static TSFM (FT)† Ours Figure 7: New-sensor performance. STAEFormer by 8.8% on PEMS07 and 33.7% on TFNSW. Appen- dix A.3.2 gives all ten datasets. High-drift periods. Figure 8 groups paired dataset-year results by drift severity. A 2 TTA improves both backbones in every quar- tile, with all 95% bootstrap intervals above zero. Gains peak in the highest sensor-churn quartile at 9.0% over Online-AN and 7.9% over STAEFormer. This legacy-batched diagnostic shows an associ- ation, not a causal effect; Appendix A.4 gives the other metrics and aggregation. 6.7 Case Study Figure 9 examines a high-variance PEMS06-2015 new sensor se- lected without using either method’s errors. Over seeds 51 and Q1 low Q2Q3Q4 high Drift-severity quartile 0 5 10 MAE reduction vs frozen (%) (a) Traffic-distribution drift Q1 low Q2Q3Q4 high Drift-severity quartile (b) Sensor churn A²TTA(OL-AN)A²TTA(STAE) Figure 8: Performance across drift-severity quartiles. 05101520 0 250 500 Traffic flow (a) Two-seed mean trace, horizon 1 05101520 0 250 500 Traffic flow (b) Two-seed mean trace, horizon 12 020406080 0 2 4 MAE gain from A2TTA (c) Two-seed mean gain vs. OL-AN 020406080 0 2 4 MAE gain from A2TTA (d) Two-seed mean gain vs. STAEFormer Positive = lower MAE PEMS06 2015 case study: sensor 601213 Ground truthOL-ANA2TTA (OL-AN)STAEFormerA2TTA (STAE) Existing sensorsNew sensors Figure 9: Two-seed case study on PEMS06-2015. 52, A 2 TTA tracks the morning rise more closely, especially at 60 minutes. Across 366 sensors, it beats Online-AN on 99.7% and STAE- Former on 98.6%, reducing mean per-sensor MAE by 7.29% and 2.62%. Appendix A.9 gives selection and cohort details. 0510152025 Elapsed deployment year −10 −1 0 10 −1 10 0 MAE improvement (%) symmetric-log y scale A 2 TTA(OLAN) vs global-only TTA 0510152025 Elapsed deployment year −10 0 −10 −1 0 10 −1 10 0 10 1 symmetric-log y scale A 2 TTA(STAE) vs global-only TTA PEMS03 PEMS04 PEMS05 PEMS06 0510152025 Elapsed deployment year 0 5 10 15 20 25 30 35 MAE improvement (%) A 2 TTA(OLAN) vs OL-AN backbone 0510152025 Elapsed deployment year 0 5 10 15 20 25 30 35 A 2 TTA(STAE) vs STAEformer backbone Long-term stability of A 2 TTA across 21–25 yearly snapshots Figure 10: Long-term five-seed stability. 6.8 Long-Term Adaptation The legacy-batched five-seed analysis in Figure 10 covers six streams over 21 to 25 years. Gains over the frozen backbone are positive A 2 TTA: Anchored-and-Agile Test-Time Adaptation for Evolving Traffic Sensor NetworksConference’17, July 2017, Washington, DC, USA every year; gains over global-only TTA are smaller and less uni- form. Appendix A.5 gives a pre-specified single-seed check on all ten datasets. Deployment cost. We profile 233 yearly snapshots on an H200. A 2 TTA(STAE) takes 11.60 ms per window versus 10.48 ms for frozen STAEFormer and raises peak allocated memory from 10,021 to 10,552 MiB. It updates 33.2K calibrator parameters on average ver- sus 2.06M backbone parameters. A 2 TTA(OLAN) takes 5.35 ms ver- sus 4.30 ms. Appendix A.6 gives the three-repeat protocol and addi- tional measurements. 7 Limitations A 2 TTA assumes that labels eventually arrive and uses a labeled training partition to warm up the calibrator for each yearly snap- shot. The main setting therefore does not cover fully label-free deployment. The new-sensor cohort contains sensors observed in the current year’s training partition and should not be interpreted as zero-shot node commissioning. A warm-up-free control in Ap- pendix A.6 measures this dependence explicitly. The evaluation is limited to univariate traffic flow, yearly graph changes, and two forecasting backbones. Absolute latency and memory also depend on the deployment hardware and graph size. 8 Conclusion We studied forecasting on evolving sensor graphs as causal delayed- feedback adaptation and introduced A 2 TTA, an output calibrator that keeps each matched yearly frozen forecaster. Its expandable FiLM module supports node growth, while persistent global and disposable local states address long-lived and context-specific shifts. The anchored global state learns persistent shifts from released la- bels, while a disposable local clone specializes to the current context and is discarded after prediction. Under one-windows chronological evaluation on nine EvoXXLTraffic districts and TFNSW, A 2 TTA improves both matched host forecasters on every dataset. Relative to the corresponding backbones, mean MAE reductions at hori- zons 3, 6, and 12 range from 9.7% to 13.2%. A 2 TTA also improves the metadata-defined new-sensor cohorts. With STAEFormer, it updates 33.2K calibrator parameters on average while leaving the 2.06M-parameter backbone unchanged, adding 1.12 ms per test window. Acknowledgments This work was supported by the ARC Centre of Excellence for Automated Decision-Making and Society (CE200100005). We ac- knowledge the resources and services provided by the National Computational Infrastructure (NCI), which is supported by the Aus- tralian Government. This research is also partially supported by the ARC Training Centre for Whole Life Design of Carbon Neutral Infrastructure (IC230100015). References [1]George EP Box, Gwilym M Jenkins, Gregory C Reinsel, and Greta M Ljung. 2015. Time series analysis: forecasting and control. John Wiley & Sons. [2]Pinlong Cai, Yunpeng Wang, Guangquan Lu, Peng Chen, Chuan Ding, and Jian- ping Sun. 2016. A spatiotemporal correlative k-nearest neighbor model for short-term traffic multistep forecasting. Transportation Research Part C: Emerging Technologies 62 (2016), 21–34. [3]Chao Chen, Karl Petty, Alexander Skabardonis, Pravin Varaiya, and Zhanfeng Jia. 2001. Freeway performance measurement system: mining loop detector data. Transportation research record 1748 (2001), 96–102. [4]Wei Chen and Yuxuan Liang. 2025. Expand and compress: Exploring tuning prin- ciples for continual spatio-temporal graph forecasting. In International Conference on Learning Representations, Vol. 2025. 81631–81656. [5]Wei Chen and Yuxuan Liang. 2025. Learning with calibration: Exploring test- time computing of spatio-temporal forecasting. Advances in Neural Information Processing Systems 38 (2025), 155895–155929. [6] Xu Chen, Junshan Wang, and Kunqing Xie. 2021. TrafficStream: A Streaming Traf- fic Flow Forecasting Framework Based on Graph Neural Networks and Continual Learning. In Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence, IJCAI-21, Zhi-Hua Zhou (Ed.). International Joint Conferences on Artificial Intelligence Organization, 3620–3626. doi:10.24963/ijcai.2021/498 Main Track. [7]Zheng Dong, Renhe Jiang, Haotian Gao, Hangchen Liu, Jinliang Deng, Qingsong Wen, and Xuan Song. 2024. Heterogeneity-informed meta-parameter learning for spatiotemporal time series forecasting. In Proceedings of the 30th ACM SIGKDD conference on knowledge discovery and data mining. 631–641. [8] Pengxin Guo, Pengrong Jin, Ziyue Li, Lei Bai, and Yu Zhang. 2024. Online Test- Time Adaptation of Spatial-Temporal Traffic Flow Forecasting. arXiv preprint arXiv:2401.04148 (2024). [9] Shengnan Guo, Youfang Lin, Ning Feng, Chao Song, and Huaiyu Wan. 2019. Attention based spatial-temporal graph convolutional networks for traffic flow forecasting. In Proceedings of the AAAI Conference on Artificial Intelligence, Vol. 33. 922–929. [10] Jiawei Jiang, Chengkai Han, Wayne Xin Zhao, and Jingyuan Wang. 2023. Pdformer: Propagation delay-aware dynamic long-range transformer for traffic flow prediction. In Proceedings of the AAAI conference on artificial intelligence, Vol. 37. 4365–4373. [11]Renhe Jiang, Du Yin, Zhaonan Wang, Yizhuo Wang, Jiewen Deng, Hangchen Liu, Zekun Cai, Jinliang Deng, Xuan Song, and Ryosuke Shibasaki. 2021. Dl-traff: Survey and benchmark of deep learning models for urban traffic prediction. In Proceedings of the 30th ACM international conference on information & knowledge management. 4515–4525. [12] Selvaraj Vasantha Kumar. 2017. Traffic flow prediction using Kalman filtering technique. Procedia Engineering 187 (2017), 582–587. [13] Yaguang Li, Rose Yu, Cyrus Shahabi, and Yan Liu. 2018. Diffusion Convolutional Recurrent Neural Network: Data-Driven Traffic Forecasting. In International Conference on Learning Representations. [14] Aoyu Liu and Yaying Zhang. 2026. A General Spatio-Temporal Backbone with Scalable Contextual Pattern Bank for Urban Continual Forecasting. In The Four- teenth International Conference on Learning Representations. [15]Hangchen Liu, Zheng Dong, Renhe Jiang, Jiewen Deng, Jinliang Deng, Quan- jun Chen, and Xuan Song. 2023. Spatio-temporal adaptive embedding makes vanilla transformer sota for traffic forecasting. In Proceedings of the 32nd ACM international conference on information and knowledge management. 4125–4129. [16]Tengfei Lyu, Weijia Zhang, Jinliang Deng, and Hao Liu. 2025. Autostf: Decoupled neural architecture search for cost-effective automated spatio-temporal forecast- ing. In Proceedings of the 31st ACM SIGKDD Conference on Knowledge Discovery and Data Mining V. 1. 985–996. [17]Haoyuan Ma, Mintao Zhou, Xiaodong Ouyang, Du Yin, Renhe Jiang, and Xuan Song. 2022. Forecasting Regional Multimodal Transportation Demand with Graph Neural Networks: An Open Dataset. In 2022 IEEE 25th International Conference on Intelligent Transportation Systems (ITSC). IEEE, 3263–3268. doi:10.1109/ITSC55140. 2022.9922512 [18]Minbo Ma, Kai Tang, Huan Li, Fei Teng, Dalin Zhang, and Tianrui Li. 2025. Beyond fixed variables: Expanding-variate time series forecasting via flat scheme and spatio-temporal focal learning. In Proceedings of the 31st ACM SIGKDD Conference on Knowledge Discovery and Data Mining V. 2. 2054–2065. [19]Florin Schimbinschi, Luis Moreira-Matias, Vinh Xuan Nguyen, and James Bailey. 2017. Topology-regularized universal vector autoregression for traffic forecasting in large urban areas. Expert Systems with Applications 82 (2017), 301–316. [20]Zezhi Shao, Zhao Zhang, Fei Wang, Wei Wei, and Yongjun Xu. 2022. Spatial- temporal identity: A simple yet effective baseline for multivariate time series forecasting. In Proceedings of the 31st ACM international conference on information & knowledge management. 4454–4458. [21] Zezhi Shao, Zhao Zhang, Wei Wei, Fei Wang, Yongjun Xu, Xin Cao, and Chris- tian S Jensen. 2022. Decoupled dynamic spatial-temporal graph neural network for traffic forecasting. Proceedings of the VLDB Endowment 15 (2022), 2733–2746. Conference’17, July 2017, Washington, DC, USAYin et al. [22]Shun-Yao Shih, Fan-Keng Sun, and Hung-yi Lee. 2019. Temporal pattern attention for multivariate time series forecasting. Machine Learning 108, 8 (2019), 1421– 1441. [23] Aaron Van Den Oord, Sander Dieleman, Heiga Zen, Karen Simonyan, Oriol Vinyals, Alex Graves, Nal Kalchbrenner, Andrew Senior, Koray Kavukcuoglu, et al. 2016. Wavenet: A generative model for raw audio. arXiv preprint arXiv:1609.03499 12, 1 (2016). [24]Binwu Wang, Yudong Zhang, Jiahao Shi, Pengkun Wang, Xu Wang, Lei Bai, and Yang Wang. 2023. Knowledge expansion and consolidation for continual traffic prediction with expanding graphs. IEEE Transactions on Intelligent Transportation Systems 24, 7 (2023), 7190–7201. [25]Binwu Wang, Yudong Zhang, Xu Wang, Pengkun Wang, Zhengyang Zhou, Lei Bai, and Yang Wang. 2023. Pattern expansion and consolidation on evolving graphs for continual traffic prediction. In Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 2223–2232. [26]Dequan Wang, Evan Shelhamer, Shaoteng Liu, Bruno Olshausen, and Trevor Darrell. 2021. Tent: Fully Test-Time Adaptation by Entropy Minimization. In International Conference on Learning Representations. [27]Billy M Williams and Lester A Hoel. 2003. Modeling and forecasting vehicular traffic flow as a seasonal ARIMA process: Theoretical basis and empirical results. Journal of transportation engineering 129, 6 (2003), 664–672. [28] Chun-Hsin Wu, Jan-Ming Ho, and Der-Tsai Lee. 2004. Travel-time prediction with support vector regression. IEEE transactions on intelligent transportation systems 5, 4 (2004), 276–281. [29]Zonghan Wu, Shirui Pan, Guodong Long, Jing Jiang, and Chengqi Zhang. 2019. Graph wavenet for deep spatial-temporal graph modeling. In Proceedings of the 28th International Joint Conference on Artificial Intelligence. 1907–1913. [30] Mingxing Xu, Wenrui Dai, Chunmiao Liu, Xing Gao, Weiyao Lin, Guo-Jun Qi, and Hongkai Xiong. 2020. Spatial-temporal transformer networks for traffic flow forecasting. arXiv preprint arXiv:2001.02908 (2020). [31]Du Yin, Jinliang Deng, Shuang Ao, Zechen Li, Hao Xue, Arian Prabowo, Renhe Jiang, Xuan Song, and Flora Salim. 2024. Enhancing Spatio-temporal Quan- tile Forecasting with Curriculum Learning: Lessons Learned. In Proceedings of the 32nd ACM International Conference on Advances in Geographic Information Systems. 42–53. [32]Du Yin, Renhe Jiang, Jiewen Deng, Yongkang Li, Yi Xie, Zhongyi Wang, Yifan Zhou, Xuan Song, and Jedi S Shang. 2023. MTMGNN: Multi-time multi-graph neural network for metro passenger flow prediction. GeoInformatica 27, 1 (2023), 77–105. [33]Du Yin, Hao Xue, Arian Prabowo, Shuang Ao, and Flora Salim. 2026. From XXLTraffic to EvoXXLTraffic: Scaling Traffic Forecasting to Sensor-Evolving Networks. arXiv preprint arXiv:2605.29768 (2026). [34]Bing Yu, Haoteng Yin, and Zhanxing Zhu. 2018. Spatio-temporal graph convolu- tional networks: a deep learning framework for traffic forecasting. In Proceedings of the 27th International Joint Conference on Artificial Intelligence. 3634–3640. [35] Haoyu Zhang, Hao Miao, Xinke Jiang, Yuchen Fang, and Yifan Zhang. 2025. Strap: Spatio-temporal pattern retrieval for out-of-distribution generalization. Advances in Neural Information Processing Systems 38 (2025), 118006–118041. [36] Ling Zhao, Yujiao Song, Chao Zhang, Yu Liu, Pu Wang, Tao Lin, Min Deng, and Haifeng Li. 2019. T-GCN: A temporal graph convolutional network for traffic prediction. IEEE transactions on intelligent transportation systems 21, 9 (2019), 3848–3858. [37]Chuanpan Zheng, Xiaoliang Fan, Cheng Wang, and Jianzhong Qi. 2020. Gman: A graph multi-attention network for traffic prediction. In Proceedings of the AAAI conference on artificial intelligence, Vol. 34. 1234–1241. A Appendix A.1 Structural Evolution Details Node counts alone do not characterize this evolution. Figure 11 therefore tracks average node degree and graph density for the yearly snapshots. Both quantities change non-monotonically, be- cause sensor additions and removals alter local neighborhoods and the set of spatial connections. Successive snapshots consequently differ in both dimension and connectivity, rather than being simple zero-padded extensions of the preceding graph. 200020052010201520202025 Year 0 200 400 600 800 1000 1200 avg. degree (edges / node) (a) Average node degree 200020052010201520202025 Year 0.0 0.1 0.2 0.3 0.4 0.5 density E / N ( N −1) (b) Graph density Structural drift of the sensor graph over time D03D04D05D06D07D08D10D11D12 Figure 11: Structural evolution of the sensor graphs. Average node degree and graph density vary across yearly snapshots, showing that graph evolution extends beyond node accumu- lation. A.2 Extended Related Work A.2.1 Spatio-Temporal Traffic Forecasting. Traffic forecasting, in- cluding traffic flow, speed, and congestion status, has always been one of the most important issues in computational urban and in- telligent transportation systems. Early traffic forecasting methods primarily relied on statistical modeling and traditional machine learning methods, such as Historical Average (HA), Autoregressive Integrated Moving Average (ARIMA) [1], Seasonal ARIMA [27], Kalman filtering [12], Vector Autoregression (VAR) [19], Support Vector Regression (SVR) [28], and푘-Nearest Neighbors (kNN) [2]. These methods typically treat traffic sequences as one-dimensional or low-dimensional time series and make predictions by modeling trends, periodicity, and short-term autocorrelation in historical ob- servations. Among them, HA uses historical averages over the same period as predictions, making it simple and efficient but difficult to adapt to sudden changes. ARIMA and its variants can character- ize linear temporal dependence and periodic patterns but usually rely on stationarity assumptions. Kalman filtering is suitable for online state estimation and short-term forecasting, while SVR and kNN improve predictive capability through nonlinear mapping or similar-pattern matching. Nevertheless, these methods mostly rely on manual feature design and struggle to characterize complex non- linear temporal variations and spatial dependencies within road networks simultaneously. Deep traffic forecasting has used convolutional neural networks (CNNs), recurrent neural networks (RNNs), graph neural networks (GNNs), Transformers, and, more recently, state-space models. Early temporal models used long short-term memory (LSTM) or gated recurrent unit (GRU) networks to capture long-range dependen- cies. CNNs [22] and temporal convolutional networks (TCNs) [23] later improved parallelism while retaining local temporal struc- ture. Graph models then made road-network dependencies explicit. Representative methods include T-GCN [36], STGCN [34], and DCRNN [13]. T-GCN places graph convolution inside GRU units, STGCN combines graph and temporal convolutions, and DCRNN models directed propagation with diffusion convolution and an encoder-decoder architecture. GNNs have also been applied to re- gional multimodal demand forecasting: Ma et al. [17] release an NYC taxi-bike dataset and study multi-source, multi-graph, and meta-information-enhanced STGNNs. Our setting instead concerns sensor graphs whose nodes and connectivity change over time. A 2 TTA: Anchored-and-Agile Test-Time Adaptation for Evolving Traffic Sensor NetworksConference’17, July 2017, Washington, DC, USA Traffic forecasting models have since developed toward adaptive graph learning, attention mechanisms, and large-scale sequence modeling. Graph WaveNet [29], for example, reduces reliance on predefined adjacency matrices by learning adaptive spatial depen- dencies. ASTGCN [9], GMAN [37], and STTN [30] introduce spatio- temporal attention to dynamically model relationships among sen- sors and time steps. Transformer-based models are now widely used because of their long-sequence modeling capability, while state-space models offer linear-complexity alternatives for large- scale forecasting. This development has produced many strong models, including MTMGNN [32], STQCL [31], STAEFormer [15], STID [20], HIMNet [7], PDFormer [10], and AutoSTF [16]. Despite their progress on static benchmarks, most existing meth- ods assume that the sensor set and road-network topology remain unchanged between training and testing. In real deployments, how- ever, sensor networks expand over time, new sensors are com- missioned, and connectivity and traffic patterns drift. A deployed forecaster therefore faces not merely a longer time series but a continuously evolving traffic graph. The resulting node growth, topology change, and temporal distribution shift challenge models built under a fixed-graph assumption. A.2.2Online and Continual Traffic Forecasting. Long-term traffic- system deployment has consequently motivated online and con- tinual forecasting. New sensors are repeatedly added, while traffic patterns at existing nodes evolve over time. An effective model must therefore acquire new spatio-temporal patterns without cata- strophically forgetting previously learned knowledge. TrafficStream [6] was among the first methods to formalize net- work expansion and pattern evolution as a streaming continual- learning problem. It uses local subgraphs to integrate neighborhood information for new sensors, Jensen–Shannon divergence to de- tect drift at existing nodes, and historical replay with parameter smoothing to mitigate catastrophic forgetting. Following an explicit- memory approach, PECPM [25] maintains a library of representa- tive spatio-temporal patterns and updates only new or conflicting nodes when a new graph arrives. STKEC [24] selects influential old nodes to construct local subgraphs, combines them with a memory bank for long-term periodic patterns, and preserves prior knowl- edge through parameter-distance regularization. To reduce update cost, EAC [4] uses a continual prompt pool to represent knowledge from different stages and follows an expansion–compression strat- egy that avoids large-scale updates of the whole model. STBP [14] freezes a general spatio-temporal backbone and expands only a scalable contextual pattern library, balancing stability and plastic- ity. STEV [18] treats new sensors as a variable-expansion problem and uses a flattening scheme to improve robustness to varying in- put scales. STRAP [35] constructs an external pattern library and retrieves similar patterns as prompts at inference time. ST-TTC [5] performs test-time calibration with frequency-domain alignment and streaming memory queues, but primarily addresses temporal drift within a fixed node set. Unlike methods that update substantial model components or de- pend on large replay memories, we adapt only a residual calibrator attached to a frozen forecaster. Records remain pending until their complete forecast horizon has elapsed. Released records update the global calibrator, and the local clone weights the retained pool by temporal phase, traffic-pattern similarity, and recency. This design handles node growth, topology change, and traffic drift without updating the deployed forecasting backbone. A.3 Complete Main Results Average performance on the remaining districts. Tables 3 and 4 add PEMS05 to PEMS08 and PEMS10 to PEMS12 to the representative results in Table 2. Across all ten networks, A 2 TTA(STAE) is the best non-foundation method in all 30 Avg dataset-metric comparisons. Averaged equally across datasets, it reduces MAE, RMSE, and MAPE over STAEFormer by 11.0%, 8.5%, and 9.7%, respectively. A 2 TTA (OLAN) improves Online-AN by 12.8%, 9.7%, and 12.2% on the same metrics. Table conventions. In Tables 3 and 4, each row is one baseline and each dataset reports MAE, RMSE, and MAPE in percent. Avg denotes the mean of cumulative-horizon scores over prediction lengths 1–12. Entries are mean±standard deviation (SD) where available and deterministic zero-shot references are single-run and shown with±0.00. Chronos-2 uses multivariate graph-grouped inference, with per-year low-rank adaptation (LoRA) for its FT variant. Bold and underlined entries mark the best and second-best non-foundation methods, respectively. Foundation-model rows are excluded from highlighting. Per-horizon performance and TSFM comparison. For compactness, the preceding tables average cumulative errors over prediction lengths 1 to 12. Tables 5 and 6 report horizons 3, 6, and 12, where A 2 TTA-S and A 2 TTA-O denote A 2 TTA(STAE) and A 2 TTA(OLAN), respectively. A 2 TTA-S is the best non-foundation method in 119 of the 120 reported cells. The exception is PEMS06 MAE at horizon 3, where A 2 TTA-O is lower. Its MAE reductions over STAEFormer average 12.1%, 10.8%, and 9.7% at horizons 3, 6, and 12. A 2 TTA-O improves Online-AN by 13.2%, 12.7%, and 12.3%. Across the three horizons and Avg rows, A 2 TTA-S also outper- forms the strongest TSFM reference in 113 of 120 cells, including all 30 Avg cells. Fine-tuning remains important for the foundation models: Chronos-2, TimesFM 2.5, and Moirai-2.0 improve over their zero-shot counterparts in all 30 Avg dataset-metric comparisons, with mean relative reductions of 13.5%, 10.9%, and 15.4%, respec- tively. Per-horizon table conventions. In Tables 5 and 6, A 2 TTA-S and A 2 TTA-O are evaluated over five seeds, and MAPE is reported in percent. Compact headers pair zero-shot and fine-tuned variants: Chro2-Z/F, TimesF-Z/T, Moira1-Z/T, and Moira2-Z/T. Determin- istic zero-shot references are single-run and shown with±0.00, whereas fine-tuned references report mean±SD over three seeds. Chronos-2 uses multivariate graph-grouped inference and per-year LoRA fine-tuning for its FT variant. TSFM columns are excluded from best/second-best highlighting. Pretrain fixes the first-year model, Retrain starts from scratch each year, Online-N updates new sensors, and Online-AN updates all active sensors. A.3.1Complete Per-Horizon Results. The main text uses PEMS03 and TFNSW for a readable per-horizon comparison. Here, we report the complete 12-step profiles for all nine EvoXXLTraffic districts and TFNSW. The curves use per-step rather than cumulative errors. The Conference’17, July 2017, Washington, DC, USAYin et al. Table 3: Average results on PEMS05–08 (mean±standard deviation). CategoryBaseline PEMS05PEMS06PEMS07PEMS08 MAERMSE MAPE (%)MAERMSE MAPE (%)MAERMSE MAPE (%)MAERMSE MAPE (%) Static STGNN Backbones DCRNN11.69 ±0.07 18.34 ±0.09 26.98 ±0.74 14.87 ±0.31 23.29 ±0.43 24.66 ±0.77 19.39 ±0.28 32.62 ±0.30 31.09 ±1.27 15.50 ±0.13 25.20 ±0.19 23.31 ±0.41 ASTGNN11.69 ±0.04 18.52 ±0.08 25.31 ±0.60 15.52 ±0.16 24.04 ±0.28 23.41 ±0.46 19.56 ±0.05 33.05 ±0.13 29.95 ±0.26 15.22 ±0.05 25.23 ±0.10 20.85 ±0.39 TGCN11.94 ±0.10 19.43 ±0.16 26.83 ±0.59 15.52 ±0.46 25.38 ±0.56 24.06 ±0.40 20.62 ±0.41 37.75 ±0.75 32.43 ±1.02 15.86 ±0.17 27.85 ±0.40 22.13 ±0.71 GWN12.57 ±0.13 19.49 ±0.18 27.19 ±0.86 16.16 ±0.54 24.84 ±0.65 24.76 ±0.81 19.51 ±0.99 32.22 ±1.35 31.81 ±2.36 15.69 ±0.16 25.27 ±0.29 21.90 ±0.74 Naïve Schemes Pretrain24.94 ±0.99 34.77 ±1.06 116.10 ±7.29 78.66 ±1.39 97.96 ±2.03 79.40 ±1.33 40.30 ±2.05 54.10 ±1.93 49.24 ±2.54 52.25 ±2.71 62.21 ±3.13 57.09 ±1.58 Retrain11.31 ±0.04 18.03 ±0.07 24.42 ±0.41 14.37 ±0.34 22.39 ±0.39 22.54 ±0.33 18.02 ±0.27 30.73 ±0.23 27.64 ±1.35 14.34 ±0.07 23.85 ±0.09 20.58 ±0.25 Online-N15.98 ±0.52 26.35 ±0.67 29.06 ±0.76 27.64 ±0.65 38.29 ±1.20 32.16 ±0.38 22.72 ±0.59 35.82 ±0.68 35.08 ±1.56 17.30 ±0.05 26.86 ±0.13 24.09 ±0.35 Online-AN 11.10 ±0.07 17.63 ±0.13 23.49 ±0.44 14.02 ±0.21 21.68 ±0.28 21.93 ±0.52 17.67 ±0.31 30.13 ±0.32 26.68 ±1.27 13.92 ±0.10 23.20 ±0.15 19.28 ±0.22 Evolving Graph TrafficStream11.32 ±0.13 18.04 ±0.14 24.56 ±0.93 14.46 ±0.34 22.41 ±0.47 22.43 ±0.49 17.54 ±0.31 30.04 ±0.29 26.67 ±2.19 14.04 ±0.13 23.35 ±0.18 20.96 ±1.33 PECPM11.67 ±0.31 18.50 ±0.44 25.13 ±0.85 18.02 ±3.19 29.03 ±6.07 26.88 ±5.50 19.23 ±1.47 32.52 ±2.46 27.85 ±1.72 15.58 ±0.77 25.25 ±1.04 22.26 ±1.64 STKEC11.48 ±0.16 18.26 ±0.21 25.11 ±0.78 14.90 ±0.24 23.19 ±0.34 24.14 ±0.58 17.07 ±1.26 29.33 ±1.84 25.66 ±3.04 14.47 ±0.38 23.89 ±0.50 21.55 ±1.34 EAC16.35 ±3.53 23.77 ±3.62 61.09 ±37.33 21.10 ±4.19 31.23 ±4.99 36.63 ±16.01 18.26 ±0.27 30.41 ±0.37 28.73 ±0.39 14.76 ±0.28 23.76 ±0.37 26.61 ±1.73 Retrieval TTC STRAP11.33 ±0.04 17.97 ±0.04 25.25 ±0.88 14.44 ±0.46 22.53 ±0.49 22.60 ±0.66 17.81 ±0.16 30.37 ±0.18 26.88 ±0.66 14.15 ±0.03 23.54 ±0.04 19.96 ±0.41 ST-TTC11.22 ±0.04 17.89 ±0.07 24.33 ±0.41 14.25 ±0.34 22.21 ±0.38 22.42 ±0.33 17.74 ±0.27 30.37 ±0.23 27.40 ±1.33 14.16 ±0.07 23.63 ±0.08 20.45 ±0.25 Static Forecasting Backbones STID11.64 ±0.06 18.69 ±0.08 24.51 ±0.52 15.39 ±0.23 24.34 ±0.40 22.72 ±0.38 19.27 ±0.19 32.22 ±0.21 34.13 ±0.84 15.12 ±0.07 25.69 ±0.17 20.33 ±0.76 STNorm12.57 ±0.10 19.00 ±0.17 35.42 ±0.64 16.70 ±0.35 24.97 ±0.45 32.58 ±1.07 25.17 ±1.15 39.57 ±1.56 58.70 ±3.03 18.33 ±0.31 28.00 ±0.33 43.33 ±2.01 iTrans11.42 ±0.06 18.04 ±0.07 24.92 ±0.37 15.18 ±0.41 23.39 ±0.46 24.00 ±0.96 18.64 ±0.09 31.19 ±0.17 30.76 ±1.13 14.60 ±0.08 23.99 ±0.13 22.07 ±0.99 DLinear12.16 ±0.05 19.40 ±0.06 26.15 ±0.70 16.40 ±0.13 25.55 ±0.15 24.49 ±0.37 19.85 ±0.01 33.90 ±0.07 29.94 ±0.50 15.58 ±0.04 26.07 ±0.04 21.16 ±0.42 STAEFormer10.16 ±0.07 16.07 ±0.10 22.83 ±0.44 13.13 ±0.60 19.88 ±0.68 20.28 ±0.85 15.32 ±0.28 26.93 ±0.26 21.39 ±0.65 12.52 ±0.03 20.88 ±0.09 17.66 ±0.23 Times-series Forecasting Foundation Model Chronos-2 (ZS)12.67 ±0.00 20.54 ±0.00 25.64 ±0.00 15.59 ±0.00 25.65 ±0.00 22.27 ±0.00 18.67 ±0.00 34.18 ±0.00 22.66 ±0.00 16.19 ±0.00 27.58 ±0.00 20.06 ±0.00 Chronos-2 (FT)11.12 ±0.01 18.61 ±0.02 21.67 ±0.02 13.66 ±0.01 23.12 ±0.04 19.42 ±0.04 16.63 ±0.04 31.15 ±0.13 20.04 ±0.03 14.22 ±0.02 25.08 ±0.08 17.49 ±0.03 TimesFM2.5 (ZS)13.11 ±0.00 21.07 ±0.00 26.75 ±0.00 16.08 ±0.00 26.22 ±0.00 22.96 ±0.00 19.55 ±0.00 35.34 ±0.00 23.68 ±0.00 16.87 ±0.00 28.38 ±0.00 20.96 ±0.00 TimesFM2.5 (FT) 11.85 ±0.01 19.92 ±0.01 22.50 ±0.02 14.28 ±0.01 24.21 ±0.01 20.06 ±0.01 17.86 ±0.02 33.57 ±0.03 21.24 ±0.02 14.90 ±0.01 26.18 ±0.02 18.26 ±0.00 Moirai-2.0 (ZS)13.26 ±0.00 21.14 ±0.00 25.93 ±0.00 16.33 ±0.00 26.23 ±0.00 22.46 ±0.00 20.58 ±0.00 36.42 ±0.00 23.57 ±0.00 17.64 ±0.00 29.31 ±0.00 20.70 ±0.00 Moirai-2.0 (FT) 11.66 ±0.00 19.31 ±0.00 23.30 ±0.01 14.28 ±0.01 23.75 ±0.04 20.71 ±0.01 17.53 ±0.01 32.42 ±0.05 21.17 ±0.03 14.99 ±0.02 25.97 ±0.06 18.63 ±0.04 Ours A2TTA(STAE)9.52 ±0.02 15.25 ±0.04 20.54 ±0.10 12.18 ±0.58 18.66 ±0.79 18.80 ±0.45 13.77 ±0.07 25.05 ±0.08 19.07 ±0.20 11.76 ±0.03 19.91 ±0.06 16.51 ±0.07 A2TTA(OLAN) 10.27 ±0.03 16.55 ±0.06 21.14 ±0.03 12.38 ±0.15 19.62 ±0.27 19.51 ±0.27 15.22 ±0.06 27.30 ±0.08 20.90 ±0.39 12.97 ±0.04 21.96 ±0.07 17.47 ±0.10 Table 4: Average results on PEMS10–12 (mean±standard deviation). CategoryBaseline PEMS10PEMS11PEMS12 MAERMSEMAPE (%)MAERMSEMAPE (%)MAERMSEMAPE (%) Static STGNN Backbones DCRNN 12.26 ±0.16 20.13 ±0.26 31.65 ±0.35 19.69 ±0.30 33.66 ±0.34 31.28 ±0.86 16.16 ±0.17 28.46 ±0.25 30.90 ±0.78 ASTGNN 12.45 ±0.05 20.80 ±0.06 30.22 ±0.32 20.00 ±0.16 34.32 ±0.27 26.69 ±0.39 15.98 ±0.10 28.49 ±0.18 27.32 ±0.53 TGCN12.43 ±0.08 21.49 ±0.14 30.86 ±0.22 21.35 ±0.31 40.11 ±0.53 30.37 ±0.32 17.13 ±0.08 33.43 ±0.19 30.68 ±0.38 GWN12.54 ±0.11 20.45 ±0.13 30.65 ±0.69 20.29 ±0.44 34.35 ±0.80 27.55 ±0.81 16.38 ±0.23 28.47 ±0.35 27.32 ±0.41 Naïve Schemes Pretrain 81.39 ±3.16 84.52 ±3.24 755.06 ±28.01 85.43 ±3.52 116.95 ±3.38 82.12 ±18.72 16.41 ±0.21 27.96 ±0.24 28.48 ±0.81 Retrain11.85 ±0.04 19.66 ±0.03 30.30 ±0.22 18.77 ±0.13 32.21 ±0.15 27.67 ±0.81 14.91 ±0.05 26.54 ±0.06 26.88 ±0.52 Online-N12.35 ±0.23 20.58 ±0.45 31.79 ±1.11 21.54 ±1.59 36.45 ±2.86 30.83 ±1.25 18.04 ±0.57 32.01 ±1.14 29.42 ±0.55 Online-AN 11.60 ±0.09 19.22 ±0.17 29.80 ±0.34 18.29 ±0.13 31.40 ±0.13 25.39 ±0.75 14.54 ±0.06 25.97 ±0.07 25.48 ±0.28 Evolving Graph TrafficStream 11.93 ±0.08 19.77 ±0.14 32.18 ±0.70 18.67 ±0.35 31.90 ±0.47 28.29 ±1.63 14.74 ±0.07 26.32 ±0.10 26.88 ±0.62 PECPM12.61 ±1.16 21.29 ±2.68 30.41 ±1.69 25.89 ±2.53 44.81 ±4.91 36.90 ±6.66 16.18 ±1.49 28.57 ±3.19 29.30 ±1.38 STKEC11.92 ±0.07 19.80 ±0.11 31.06 ±0.42 19.02 ±0.23 32.38 ±0.23 30.78 ±1.62 14.71 ±0.08 26.28 ±0.12 26.66 ±0.60 EAC13.60 ±1.76 21.08 ±1.43 59.52 ±40.27 25.76 ±4.14 41.08 ±5.52 47.34 ±12.72 14.98 ±0.30 26.18 ±0.40 29.71 ±2.65 Retrieval TTC STRAP 11.79 ±0.09 19.58 ±0.10 30.34 ±0.58 18.60 ±0.15 31.88 ±0.20 28.85 ±1.00 14.88 ±0.14 26.48 ±0.17 27.09 ±1.22 ST-TTC11.76 ±0.04 19.53 ±0.04 30.14 ±0.22 18.52 ±0.13 31.83 ±0.15 27.53 ±0.80 14.74 ±0.05 26.28 ±0.05 26.77 ±0.51 Static Forecasting Backbones STID12.53 ±0.08 20.54 ±0.09 33.11 ±0.25 20.02 ±0.32 33.89 ±0.36 32.17 ±1.75 16.07 ±0.07 28.14 ±0.19 33.77 ±0.88 STNorm13.75 ±0.32 21.81 ±0.40 41.57 ±1.79 21.77 ±0.34 35.62 ±0.53 48.00 ±2.68 19.49 ±0.39 32.19 ±0.51 58.93 ±2.28 iTrans11.83 ±0.07 19.63 ±0.10 30.28 ±0.74 19.24 ±0.28 32.79 ±0.31 30.95 ±2.77 15.27 ±0.11 26.92 ±0.15 29.32 ±1.41 DLinear12.86 ±0.04 21.36 ±0.05 31.07 ±0.38 20.62 ±0.12 35.52 ±0.13 27.66 ±0.61 16.23 ±0.02 29.24 ±0.05 27.74 ±0.47 STAEFormer10.34 ±0.03 17.20 ±0.05 27.83 ±0.45 17.05 ±0.12 28.82 ±0.20 24.54 ±0.69 12.91 ±0.11 23.13 ±0.12 23.94 ±0.74 Times-series Forecasting Foundation Model Chronos-2 (ZS)13.30 ±0.00 22.54 ±0.00 30.51 ±0.00 20.04 ±0.00 37.05 ±0.00 25.36 ±0.00 16.67 ±0.00 30.85 ±0.00 26.63 ±0.00 Chronos-2 (FT) 11.85 ±0.01 20.64 ±0.04 27.84 ±0.07 17.19 ±0.02 32.41 ±0.08 21.93 ±0.04 14.66 ±0.01 27.68 ±0.07 22.84 ±0.04 TimesFM2.5 (ZS) 13.63 ±0.00 22.92 ±0.00 31.47 ±0.00 20.91 ±0.00 38.14 ±0.00 26.41 ±0.00 17.48 ±0.00 31.92 ±0.00 27.93 ±0.00 TimesFM2.5 (FT) 12.27 ±0.01 21.11 ±0.01 28.62 ±0.03 18.32 ±0.02 34.43 ±0.07 23.11 ±0.03 15.69 ±0.02 29.74 ±0.05 24.31 ±0.02 Moirai-2.0 (ZS) 14.18 ±0.00 23.64 ±0.00 30.73 ±0.00 21.24 ±0.00 38.56 ±0.00 25.78 ±0.00 17.90 ±0.00 32.32 ±0.00 27.26 ±0.00 Moirai-2.0 (FT) 12.43 ±0.01 21.32 ±0.03 29.22 ±0.02 17.71 ±0.01 32.78 ±0.04 23.23 ±0.03 15.32 ±0.01 28.62 ±0.02 24.38 ±0.02 Ours A2TTA(STAE)9.86 ±0.03 16.58 ±0.03 26.41 ±0.04 14.40 ±0.07 25.74 ±0.10 21.44 ±0.25 11.95 ±0.05 21.71 ±0.08 21.98 ±0.24 A2TTA(OLAN)10.88 ±0.04 18.28 ±0.08 27.73 ±0.07 15.60 ±0.08 28.06 ±0.13 23.73 ±0.38 13.28 ±0.01 24.05 ±0.02 23.36 ±0.11 A 2 TTA curves follow the one-window delayed-feedback protocol used by the main runs. All sensors. As shown in fig. 12, A 2 TTA(STAE) has the lowest error among the six plotted methods in all 10×3×12=360 combinations. Averaged over dataset and horizon, it improves on frozen STAEFormer by 9.7% in MAE, 7.3% in RMSE, and 9.3% in MAPE. A.3.2 Detailed Results on Newly Added Sensors. A 2 TTA: Anchored-and-Agile Test-Time Adaptation for Evolving Traffic Sensor NetworksConference’17, July 2017, Washington, DC, USA Table 5: Main experimental results, part 1/2 (PEMS03, PEMS04, PEMS05, PEMS06, PEMS07, PEMS08, PEMS10, PEMS11; mean±std over seeds per dataset). Bold: best,underline: second best. A2TTA-S and A2TTA-O are measured over 5 seeds. MAPE values are reported in percent. Chronos-2 (ZS) and Chronos-2 (FT) use multivariate graph-grouped inference; FT uses per-year LoRA fine-tuning. TSFM columns are excluded from highlighting. Compact headers denote zero-shot/fine-tuned pairs: Chro2-Z/F for Chronos-2, TimesF-Z/T for TimesFM2.5, Moira1-Z/T for Moirai-MoE, and Moira2-Z/T for Moirai-2.0. Their deterministic zero-shot (ZS) references are single-run and shown with±0.00 for visual consistency; fine-tuned (FT) references are reported as mean±std over 3 seeds. Static STGNN BackbonesNaïve SchemesEvolving GraphRetrieval TTCStatic Forecasting BackbonesTSFMsOurs Metric Len DCRNN ASTGNN TGCN GWN Pretrain Retrain OL-N OL-AN TrafStm PECPM STKEC EAC STRAP ST-TTC STID STNorm iTrans DLinear STAE Chro2-Z Chro2-F TimesF-Z TimesF-T Moira1-Z Moira1-T Moira2-Z Moira2-T A2TTA-S A2TTA-O PEMS03 MAE 314.42 ±0.21 13.70 ±0.12 15.14 ±0.10 14.22 ±0.29 30.61 ±1.22 13.09 ±0.16 16.25 ±0.19 12.76 ±0.05 13.22 ±0.11 13.88 ±0.85 13.42 ±0.27 14.18 ±0.31 13.10 ±0.12 12.89 ±0.15 14.28 ±0.15 16.46 ±0.42 13.16 ±0.13 14.17 ±0.07 11.81 ±0.11 12.53 ±0.00 11.73 ±0.01 13.20 ±0.00 12.13 ±0.01 14.50 ±0.00 16.03 ±0.64 13.66 ±0.00 12.16 ±0.00 10.57 ±0.03 11.18 ±0.03 614.67 ±0.18 14.89 ±0.10 15.63 ±0.10 15.08 ±0.23 31.21 ±1.19 14.01 ±0.14 17.32 ±0.16 13.68 ±0.05 14.17 ±0.17 14.76 ±0.81 14.28 ±0.20 15.64 ±0.48 14.00 ±0.12 13.82 ±0.13 14.89 ±0.14 17.86 ±0.45 14.05 ±0.14 15.45 ±0.06 12.22 ±0.10 14.74 ±0.00 13.09 ±0.01 15.55 ±0.00 13.87 ±0.01 17.22 ±0.00 18.39 ±0.59 15.87 ±0.00 13.70 ±0.01 11.08 ±0.03 12.10 ±0.04 1216.27 ±0.18 17.57 ±0.08 17.27 ±0.11 17.24 ±0.30 32.66 ±0.99 15.92 ±0.14 19.41 ±0.20 15.46 ±0.09 16.10 ±0.35 16.57 ±0.78 16.24 ±0.18 18.65 ±0.79 15.86 ±0.15 15.74 ±0.13 16.71 ±0.13 21.02 ±0.59 15.95 ±0.13 18.34 ±0.04 12.98 ±0.13 19.88 ±0.00 15.90 ±0.02 20.21 ±0.00 17.38 ±0.02 22.10 ±0.00 22.80 ±0.59 20.35 ±0.00 16.86 ±0.01 11.93 ±0.05 13.74 ±0.07 Avg 14.99 ±0.18 15.15 ±0.10 15.88 ±0.10 15.33 ±0.26 31.37 ±1.11 14.16 ±0.15 17.47 ±0.16 13.80 ±0.05 14.32 ±0.20 14.90 ±0.81 14.47 ±0.22 15.91 ±0.48 14.15 ±0.13 13.98 ±0.14 15.14 ±0.14 18.20 ±0.47 14.21 ±0.13 15.73 ±0.06 12.26 ±0.11 15.27 ±0.00 13.31 ±0.01 15.91 ±0.00 14.16 ±0.01 17.59 ±0.00 18.68 ±0.59 16.19 ±0.00 13.95 ±0.01 11.10 ±0.04 12.19 ±0.04 RMSE 323.64 ±0.22 22.30 ±0.20 28.88 ±0.42 23.01 ±0.41 39.61 ±1.17 21.27 ±0.15 25.71 ±0.14 20.83 ±0.06 21.39 ±0.10 22.19 ±1.02 21.71 ±0.38 22.90 ±0.58 21.23 ±0.22 20.98 ±0.13 25.67 ±0.42 25.72 ±0.59 21.37 ±0.14 23.03 ±0.04 19.61 ±0.15 21.37 ±0.00 20.23 ±0.02 22.46 ±0.00 20.93 ±0.03 25.10 ±0.00 27.89 ±1.02 23.21 ±0.00 20.77 ±0.02 17.79 ±0.06 18.79 ±0.05 624.33 ±0.17 24.71 ±0.16 29.72 ±0.40 24.70 ±0.33 41.30 ±1.09 23.20 ±0.12 28.00 ±0.10 22.70 ±0.10 23.35 ±0.22 24.08 ±0.95 23.56 ±0.28 25.90 ±0.88 23.13 ±0.21 22.93 ±0.11 26.68 ±0.38 27.99 ±0.61 23.14 ±0.15 25.74 ±0.04 20.52 ±0.12 25.87 ±0.00 23.16 ±0.04 27.14 ±0.00 24.74 ±0.04 30.33 ±0.00 32.52 ±0.89 27.41 ±0.00 23.96 ±0.03 18.88 ±0.07 20.62 ±0.07 1227.56 ±0.21 29.82 ±0.14 32.46 ±0.37 28.79 ±0.51 44.99 ±0.98 26.94 ±0.16 32.37 ±0.35 26.14 ±0.20 27.11 ±0.58 27.75 ±0.94 27.50 ±0.37 31.87 ±1.46 26.81 ±0.26 26.70 ±0.15 29.78 ±0.35 33.28 ±0.82 26.74 ±0.15 31.45 ±0.04 22.05 ±0.13 36.36 ±0.00 29.28 ±0.07 36.42 ±0.00 32.31 ±0.09 39.29 ±0.00 40.97 ±0.93 35.98 ±0.00 30.56 ±0.04 20.50 ±0.08 23.65 ±0.12 Avg 24.90 ±0.19 25.15 ±0.17 30.12 ±0.40 25.15 ±0.39 41.64 ±0.99 23.46 ±0.14 28.29 ±0.08 22.89 ±0.11 23.60 ±0.28 24.32 ±0.98 23.89 ±0.34 26.40 ±0.88 23.37 ±0.22 23.18 ±0.13 27.10 ±0.38 28.58 ±0.65 23.42 ±0.14 26.23 ±0.04 20.58 ±0.12 26.98 ±0.00 23.66 ±0.03 27.86 ±0.00 25.36 ±0.04 30.92 ±0.00 32.99 ±0.89 28.00 ±0.00 24.51 ±0.03 18.87 ±0.07 20.72 ±0.07 MAPE (%) 328.08 ±0.88 24.72 ±0.40 28.13 ±0.82 26.65 ±0.67 50.48 ±2.93 25.11 ±0.64 28.43 ±0.78 24.05 ±0.22 26.49 ±1.13 26.87 ±2.27 26.48 ±0.70 27.89 ±1.36 25.03 ±0.27 24.96 ±0.64 25.31 ±0.62 49.62 ±2.31 25.56 ±0.78 26.28 ±0.91 22.52 ±0.64 22.59 ±0.00 21.07 ±0.03 23.53 ±0.00 21.74 ±0.02 23.11 ±0.00 23.82 ±0.36 23.23 ±0.00 22.00 ±0.01 20.86 ±0.18 22.34 ±0.26 628.30 ±0.86 26.15 ±0.42 28.46 ±0.91 27.65 ±0.69 49.81 ±2.94 26.03 ±0.57 29.35 ±0.93 24.75 ±0.17 27.29 ±1.48 27.58 ±2.27 27.28 ±0.67 29.56 ±0.89 25.82 ±0.29 25.89 ±0.57 26.15 ±0.61 52.24 ±2.52 26.53 ±0.74 27.99 ±0.96 22.95 ±0.64 25.06 ±0.00 22.52 ±0.03 26.19 ±0.00 23.46 ±0.02 25.83 ±0.00 26.96 ±0.32 25.68 ±0.00 23.83 ±0.01 21.37 ±0.18 23.27 ±0.26 1230.21 ±0.81 29.78 ±0.50 30.89 ±0.96 30.44 ±0.82 49.61 ±2.26 28.34 ±0.49 31.64 ±1.66 26.62 ±0.25 29.70 ±2.58 29.44 ±2.39 29.57 ±0.77 34.17 ±1.00 28.11 ±0.57 28.20 ±0.48 28.48 ±0.63 58.49 ±3.04 28.91 ±0.60 32.53 ±1.08 24.00 ±0.63 31.43 ±0.00 25.67 ±0.02 31.92 ±0.00 27.12 ±0.01 31.32 ±0.00 32.00 ±0.24 30.84 ±0.00 27.77 ±0.03 22.44 ±0.20 25.20 ±0.30 Avg 28.69 ±0.86 26.56 ±0.43 28.95 ±0.89 28.01 ±0.71 50.04 ±2.80 26.29 ±0.58 29.62 ±1.04 24.96 ±0.21 27.63 ±1.67 27.78 ±2.30 27.58 ±0.64 30.12 ±0.81 26.12 ±0.31 26.15 ±0.57 26.44 ±0.62 52.94 ±2.57 26.79 ±0.71 28.55 ±0.98 23.06 ±0.64 25.83 ±0.00 22.80 ±0.03 26.71 ±0.00 23.79 ±0.01 26.24 ±0.00 27.23 ±0.31 26.15 ±0.00 24.18 ±0.01 21.46 ±0.18 23.43 ±0.27 PEMS04 MAE 321.15 ±0.32 20.23 ±0.12 22.27 ±0.38 22.00 ±0.32 153.31 ±6.85 19.92 ±0.23 36.81 ±0.33 19.34 ±0.22 19.74 ±0.48 23.62 ±3.33 21.20 ±1.34 31.75 ±9.85 20.31 ±0.70 19.59 ±0.23 21.19 ±0.21 22.37 ±0.62 19.59 ±0.15 21.27 ±0.23 18.62 ±0.99 17.60 ±0.00 16.52 ±0.03 19.32 ±0.00 17.78 ±0.02 21.81 ±0.00 26.08 ±0.33 20.63 ±0.00 17.86 ±0.03 15.81 ±0.07 16.56 ±0.04 621.75 ±0.26 22.06 ±0.11 23.22 ±0.37 22.97 ±0.28 153.21 ±6.57 21.35 ±0.19 38.21 ±0.32 20.78 ±0.26 21.18 ±0.50 24.90 ±3.16 22.41 ±1.06 33.61 ±9.31 21.63 ±0.64 21.04 ±0.19 21.96 ±0.17 23.63 ±0.63 20.94 ±0.11 23.12 ±0.17 19.33 ±0.95 20.75 ±0.00 18.59 ±0.04 22.92 ±0.00 20.46 ±0.02 26.14 ±0.00 30.01 ±0.17 24.04 ±0.00 20.27 ±0.03 16.65 ±0.11 18.01 ±0.04 1224.38 ±0.25 26.11 ±0.06 25.97 ±0.36 26.06 ±0.26 153.51 ±6.60 24.45 ±0.19 41.12 ±0.17 23.68 ±0.33 24.16 ±0.63 27.74 ±2.99 25.55 ±1.01 37.67 ±7.70 24.64 ±0.65 24.17 ±0.18 24.86 ±0.16 26.74 ±0.68 23.91 ±0.11 27.45 ±0.13 20.61 ±0.94 28.27 ±0.00 22.84 ±0.07 30.08 ±0.00 25.86 ±0.01 33.86 ±0.00 39.47 ±0.65 30.91 ±0.00 25.23 ±0.02 18.06 ±0.18 20.62 ±0.08 Avg 22.22 ±0.27 22.45 ±0.09 23.60 ±0.37 23.41 ±0.27 153.33 ±6.62 21.64 ±0.20 38.46 ±0.27 21.01 ±0.26 21.43 ±0.53 25.16 ±3.18 22.78 ±1.14 34.02 ±9.03 21.93 ±0.67 21.33 ±0.20 22.43 ±0.18 23.99 ±0.62 21.22 ±0.11 23.58 ±0.18 19.38 ±0.94 21.58 ±0.00 18.94 ±0.04 23.49 ±0.00 20.92 ±0.02 26.72 ±0.00 31.16 ±0.33 24.52 ±0.00 20.68 ±0.03 16.70 ±0.11 18.15 ±0.05 RMSE 332.49 ±0.37 31.23 ±0.11 36.57 ±0.57 33.27 ±0.26 185.75 ±7.85 30.57 ±0.22 48.99 ±0.57 29.87 ±0.23 30.41 ±0.49 36.55 ±4.40 31.87 ±1.33 44.57 ±11.20 30.86 ±0.67 30.17 ±0.22 33.49 ±0.37 34.23 ±0.76 30.24 ±0.20 32.51 ±0.25 29.26 ±1.26 28.79 ±0.00 27.45 ±0.07 30.99 ±0.00 29.58 ±0.02 34.99 ±0.00 41.11 ±0.57 32.99 ±0.00 29.40 ±0.11 25.94 ±0.11 27.03 ±0.04 633.93 ±0.28 34.42 ±0.10 38.28 ±0.55 35.06 ±0.24 186.05 ±7.49 33.18 ±0.20 51.49 ±0.51 32.43 ±0.30 33.00 ±0.54 38.80 ±4.09 34.23 ±1.05 47.58 ±10.31 33.36 ±0.61 32.80 ±0.20 34.98 ±0.29 36.16 ±0.79 32.65 ±0.16 35.90 ±0.21 30.61 ±1.20 33.78 ±0.00 31.20 ±0.10 36.72 ±0.00 34.39 ±0.01 41.80 ±0.00 47.11 ±0.31 38.04 ±0.00 33.63 ±0.09 27.44 ±0.14 29.43 ±0.07 1238.46 ±0.30 40.98 ±0.17 42.75 ±0.53 40.07 ±0.30 187.60 ±7.68 38.43 ±0.24 56.38 ±0.30 37.23 ±0.45 37.99 ±0.82 43.47 ±3.76 39.70 ±1.19 53.93 ±7.70 38.50 ±0.67 38.08 ±0.25 39.67 ±0.26 40.75 ±0.93 37.57 ±0.19 43.10 ±0.21 32.76 ±1.20 46.16 ±0.00 39.07 ±0.21 48.32 ±0.00 43.96 ±0.03 53.81 ±0.00 64.62 ±2.50 48.84 ±0.00 42.50 ±0.06 29.73 ±0.25 33.51 ±0.13 Avg 34.58 ±0.32 34.96 ±0.12 38.82 ±0.55 35.69 ±0.22 186.37 ±7.58 33.58 ±0.22 51.85 ±0.46 32.73 ±0.31 33.35 ±0.60 39.17 ±4.12 34.78 ±1.18 48.20 ±9.87 33.78 ±0.64 33.21 ±0.22 35.63 ±0.31 36.65 ±0.80 33.04 ±0.17 36.54 ±0.22 30.64 ±1.20 35.22 ±0.00 31.89 ±0.12 37.69 ±0.00 35.20 ±0.02 42.74 ±0.00 49.27 ±0.58 38.87 ±0.00 34.42 ±0.09 27.46 ±0.15 29.59 ±0.07 MAPE (%) 319.95 ±0.41 17.57 ±0.43 19.35 ±0.26 18.96 ±0.52 82.38 ±3.00 17.87 ±0.35 25.59 ±0.52 16.67 ±0.26 17.63 ±0.50 21.16 ±3.83 20.61 ±1.82 37.87 ±18.81 18.37 ±0.71 17.74 ±0.35 17.69 ±0.30 26.18 ±1.42 18.27 ±0.21 17.68 ±0.31 16.44 ±0.94 14.71 ±0.00 13.71 ±0.01 16.27 ±0.00 14.69 ±0.02 16.45 ±0.00 17.91 ±0.07 16.23 ±0.00 14.90 ±0.01 14.27 ±0.03 15.20 ±0.22 620.17 ±0.42 18.89 ±0.42 19.76 ±0.28 19.60 ±0.54 82.26 ±3.00 18.86 ±0.28 26.67 ±0.66 17.58 ±0.32 18.53 ±0.54 22.08 ±3.77 21.21 ±1.50 38.74 ±17.46 19.14 ±0.60 18.75 ±0.28 18.18 ±0.26 27.56 ±1.51 19.11 ±0.24 19.09 ±0.32 16.86 ±0.94 16.93 ±0.00 15.00 ±0.01 18.84 ±0.00 16.33 ±0.02 19.03 ±0.00 20.80 ±0.03 18.75 ±0.00 16.48 ±0.02 14.81 ±0.04 16.25 ±0.28 1221.91 ±0.40 22.29 ±0.42 21.86 ±0.33 21.79 ±0.59 82.01 ±3.01 21.34 ±0.25 29.13 ±1.08 19.79 ±0.43 20.92 ±0.83 24.23 ±3.51 23.44 ±1.32 42.12 ±15.90 21.54 ±0.39 21.24 ±0.24 20.14 ±0.21 31.05 ±1.68 21.23 ±0.34 22.99 ±0.46 17.90 ±1.02 22.62 ±0.00 17.78 ±0.01 24.24 ±0.00 19.78 ±0.02 23.86 ±0.00 26.17 ±0.16 23.60 ±0.00 19.89 ±0.03 15.90 ±0.09 18.36 ±0.38 Avg 20.53 ±0.40 19.29 ±0.42 20.15 ±0.28 19.94 ±0.55 82.25 ±2.99 19.15 ±0.30 26.93 ±0.71 17.82 ±0.31 18.83 ±0.59 22.29 ±3.69 21.54 ±1.53 39.19 ±17.54 19.49 ±0.57 19.04 ±0.29 18.51 ±0.26 27.98 ±1.51 19.36 ±0.25 19.60 ±0.33 16.97 ±0.95 17.62 ±0.00 15.25 ±0.01 19.32 ±0.00 16.65 ±0.02 19.38 ±0.00 21.25 ±0.07 19.11 ±0.00 16.78 ±0.02 14.89 ±0.05 16.41 ±0.28 PEMS05 MAE 311.22 ±0.09 10.77 ±0.03 11.31 ±0.11 11.71 ±0.12 24.31 ±1.08 10.54 ±0.04 14.56 ±0.51 10.39 ±0.07 10.54 ±0.12 10.93 ±0.34 10.73 ±0.17 15.58 ±3.35 10.58 ±0.05 10.45 ±0.04 11.03 ±0.07 11.98 ±0.14 10.69 ±0.07 11.00 ±0.06 9.88 ±0.06 10.72 ±0.00 10.01 ±0.01 11.20 ±0.00 10.44 ±0.01 12.13 ±0.00 13.76 ±0.38 11.56 ±0.00 10.39 ±0.00 9.20 ±0.02 9.63 ±0.01 611.49 ±0.06 11.55 ±0.04 11.79 ±0.09 12.34 ±0.13 24.77 ±0.99 11.20 ±0.04 15.76 ±0.54 11.00 ±0.07 11.21 ±0.12 11.55 ±0.31 11.36 ±0.14 16.21 ±3.54 11.21 ±0.03 11.11 ±0.04 11.48 ±0.05 12.44 ±0.11 11.30 ±0.06 11.96 ±0.05 10.12 ±0.07 12.23 ±0.00 10.94 ±0.01 12.84 ±0.00 11.62 ±0.01 14.04 ±0.00 15.48 ±0.25 12.97 ±0.00 11.46 ±0.00 9.50 ±0.02 10.21 ±0.03 1212.63 ±0.05 13.21 ±0.05 13.04 ±0.08 14.10 ±0.18 26.01 ±1.05 12.57 ±0.06 18.26 ±0.54 12.24 ±0.11 12.57 ±0.16 12.87 ±0.27 12.72 ±0.17 17.64 ±3.79 12.55 ±0.05 12.48 ±0.06 12.72 ±0.05 13.56 ±0.08 12.62 ±0.05 14.06 ±0.06 10.60 ±0.08 15.95 ±0.00 12.93 ±0.02 16.14 ±0.00 14.09 ±0.01 17.55 ±0.00 18.96 ±0.26 16.18 ±0.00 13.73 ±0.00 10.01 ±0.04 11.28 ±0.05 Avg 11.69 ±0.07 11.69 ±0.04 11.94 ±0.10 12.57 ±0.13 24.94 ±0.99 11.31 ±0.04 15.98 ±0.52 11.10 ±0.07 11.32 ±0.13 11.67 ±0.31 11.48 ±0.16 16.35 ±3.53 11.33 ±0.04 11.22 ±0.04 11.64 ±0.06 12.57 ±0.10 11.42 ±0.06 12.16 ±0.05 10.16 ±0.07 12.67 ±0.00 11.12 ±0.01 13.11 ±0.00 11.85 ±0.01 14.34 ±0.00 15.75 ±0.28 13.26 ±0.00 11.66 ±0.00 9.52 ±0.02 10.27 ±0.03 RMSE 317.36 ±0.11 16.92 ±0.07 18.29 ±0.18 17.96 ±0.15 33.60 ±1.18 16.59 ±0.07 23.55 ±0.72 16.33 ±0.09 16.61 ±0.11 17.14 ±0.48 16.84 ±0.20 22.45 ±3.39 16.58 ±0.06 16.46 ±0.06 17.64 ±0.10 18.03 ±0.22 16.69 ±0.08 17.33 ±0.06 15.54 ±0.09 17.14 ±0.00 16.31 ±0.01 17.78 ±0.00 16.98 ±0.00 19.54 ±0.00 21.76 ±0.54 18.39 ±0.00 16.77 ±0.01 14.67 ±0.03 15.41 ±0.03 618.03 ±0.07 18.31 ±0.07 19.20 ±0.16 19.12 ±0.18 34.52 ±1.07 17.84 ±0.06 25.94 ±0.75 17.49 ±0.13 17.87 ±0.12 18.33 ±0.43 18.07 ±0.18 23.58 ±3.68 17.79 ±0.05 17.71 ±0.06 18.43 ±0.07 18.81 ±0.16 17.86 ±0.07 19.09 ±0.05 16.02 ±0.10 19.78 ±0.00 18.19 ±0.01 20.61 ±0.00 19.44 ±0.01 22.68 ±0.00 24.70 ±0.40 20.68 ±0.00 18.85 ±0.01 15.24 ±0.04 16.48 ±0.05 1220.16 ±0.08 21.07 ±0.10 21.40 ±0.15 22.14 ±0.27 36.72 ±1.19 20.30 ±0.12 30.76 ±0.61 19.68 ±0.22 20.32 ±0.22 20.68 ±0.38 20.57 ±0.27 25.93 ±3.97 20.19 ±0.09 20.17 ±0.12 20.58 ±0.06 20.61 ±0.16 20.20 ±0.08 22.73 ±0.08 16.89 ±0.13 26.27 ±0.00 22.43 ±0.04 26.26 ±0.00 24.56 ±0.02 28.35 ±0.00 30.31 ±0.41 25.89 ±0.00 23.50 ±0.02 16.13 ±0.06 18.33 ±0.10 Avg 18.34 ±0.09 18.52 ±0.08 19.43 ±0.16 19.49 ±0.18 34.77 ±1.06 18.03 ±0.07 26.35 ±0.67 17.63 ±0.13 18.04 ±0.14 18.50 ±0.44 18.26 ±0.21 23.77 ±3.62 17.97 ±0.04 17.89 ±0.07 18.69 ±0.08 19.00 ±0.17 18.04 ±0.07 19.40 ±0.06 16.07 ±0.10 20.54 ±0.00 18.61 ±0.02 21.07 ±0.00 19.92 ±0.01 23.12 ±0.00 25.07 ±0.41 21.14 ±0.00 19.31 ±0.00 15.25 ±0.04 16.55 ±0.06 MAPE (%) 326.28 ±0.86 23.31 ±0.62 25.81 ±0.68 25.60 ±0.88 114.78 ±6.27 23.06 ±0.42 27.15 ±0.88 22.28 ±0.43 23.18 ±0.88 23.88 ±0.92 23.69 ±0.81 59.98 ±37.51 23.90 ±0.94 22.97 ±0.42 23.40 ±0.55 33.91 ±0.52 23.53 ±0.44 23.50 ±0.68 22.26 ±0.46 21.96 ±0.00 20.12 ±0.01 23.23 ±0.00 20.62 ±0.02 22.62 ±0.00 23.96 ±0.28 22.69 ±0.00 21.26 ±0.01 19.94 ±0.11 20.14 ±0.06 626.59 ±0.75 24.92 ±0.62 26.46 ±0.61 26.73 ±0.88 115.48 ±6.90 24.15 ±0.42 28.67 ±0.81 23.24 ±0.42 24.29 ±0.95 24.84 ±0.87 24.82 ±0.74 60.44 ±37.27 24.93 ±0.92 24.05 ±0.42 24.20 ±0.51 35.01 ±0.59 24.65 ±0.36 25.54 ±0.69 22.67 ±0.37 24.72 ±0.00 21.39 ±0.01 26.15 ±0.00 22.15 ±0.01 25.53 ±0.00 27.63 ±0.14 25.33 ±0.00 22.97 ±0.01 20.45 ±0.09 21.01 ±0.02 1228.62 ±0.63 28.72 ±0.60 28.84 ±0.49 30.08 ±0.80 118.51 ±8.78 26.77 ±0.42 32.35 ±0.78 25.61 ±0.55 26.89 ±1.00 27.37 ±0.73 27.67 ±0.80 63.79 ±37.30 27.61 ±0.75 26.67 ±0.42 26.50 ±0.51 38.11 ±0.99 27.28 ±0.38 30.73 ±0.73 23.86 ±0.49 32.01 ±0.00 24.30 ±0.03 32.54 ±0.00 25.58 ±0.01 31.30 ±0.00 33.24 ±0.06 31.29 ±0.00 26.70 ±0.01 21.51 ±0.11 22.78 ±0.04 Avg 26.98 ±0.74 25.31 ±0.60 26.83 ±0.59 27.19 ±0.86 116.10 ±7.29 24.42 ±0.41 29.06 ±0.76 23.49 ±0.44 24.56 ±0.93 25.13 ±0.85 25.11 ±0.78 61.09 ±37.33 25.25 ±0.88 24.33 ±0.41 24.51 ±0.52 35.42 ±0.64 24.92 ±0.37 26.15 ±0.70 22.83 ±0.44 25.64 ±0.00 21.67 ±0.02 26.75 ±0.00 22.50 ±0.02 25.96 ±0.00 27.92 ±0.16 25.93 ±0.00 23.30 ±0.01 20.54 ±0.10 21.14 ±0.03 PEMS06 MAE 314.29 ±0.34 14.25 ±0.15 14.75 ±0.46 14.91 ±0.58 78.18 ±1.49 13.39 ±0.36 26.65 ±0.40 13.10 ±0.23 13.47 ±0.33 17.23 ±3.32 13.86 ±0.26 19.38 ±4.55 13.53 ±0.45 13.28 ±0.36 14.65 ±0.27 15.70 ±0.34 14.19 ±0.45 14.86 ±0.15 12.73 ±0.61 13.03 ±0.00 12.20 ±0.01 13.60 ±0.00 12.46 ±0.01 14.70 ±0.00 17.57 ±0.43 14.03 ±0.00 12.68 ±0.01 11.73 ±0.57 11.50 ±0.14 614.60 ±0.30 15.36 ±0.17 15.33 ±0.46 15.92 ±0.53 78.77 ±1.35 14.24 ±0.34 27.53 ±0.65 13.91 ±0.21 14.33 ±0.33 17.90 ±3.21 14.75 ±0.23 20.83 ±4.24 14.30 ±0.46 14.13 ±0.34 15.20 ±0.21 16.52 ±0.33 15.02 ±0.42 16.16 ±0.13 13.09 ±0.61 15.11 ±0.00 13.47 ±0.01 15.79 ±0.00 14.02 ±0.01 17.33 ±0.00 19.73 ±0.46 16.01 ±0.00 14.08 ±0.01 12.15 ±0.58 12.31 ±0.16 1216.11 ±0.30 17.62 ±0.22 16.90 ±0.44 18.24 ±0.51 79.36 ±1.36 15.99 ±0.31 29.23 ±1.05 15.54 ±0.26 16.09 ±0.35 19.37 ±2.99 16.67 ±0.21 23.88 ±3.70 15.99 ±0.52 15.88 ±0.32 16.77 ±0.20 18.34 ±0.40 16.83 ±0.37 18.94 ±0.11 13.78 ±0.56 19.88 ±0.00 16.06 ±0.01 20.01 ±0.00 17.21 ±0.01 22.01 ±0.00 24.25 ±0.31 20.28 ±0.00 16.91 ±0.01 12.88 ±0.58 13.77 ±0.18 Avg 14.87 ±0.31 15.52 ±0.16 15.52 ±0.46 16.16 ±0.54 78.66 ±1.39 14.37 ±0.34 27.64 ±0.65 14.02 ±0.21 14.46 ±0.34 18.02 ±3.19 14.90 ±0.24 21.10 ±4.19 14.44 ±0.46 14.25 ±0.34 15.39 ±0.23 16.70 ±0.35 15.18 ±0.41 16.40 ±0.13 13.13 ±0.60 15.59 ±0.00 13.66 ±0.01 16.08 ±0.00 14.28 ±0.01 17.67 ±0.00 20.04 ±0.40 16.33 ±0.00 14.28 ±0.01 12.18 ±0.58 12.38 ±0.15 RMSE 322.13 ±0.48 21.74 ±0.27 23.99 ±0.57 22.66 ±0.70 96.67 ±2.18 20.57 ±0.42 36.24 ±0.70 20.00 ±0.18 20.57 ±0.42 27.60 ±6.52 21.19 ±0.35 28.19 ±5.72 20.82 ±0.45 20.39 ±0.41 23.12 ±0.45 23.42 ±0.45 21.56 ±0.48 22.68 ±0.15 19.15 ±0.71 20.74 ±0.00 19.77 ±0.05 21.65 ±0.00 20.03 ±0.02 23.69 ±0.00 27.96 ±0.62 22.24 ±0.00 20.34 ±0.02 17.89 ±0.81 17.96 ±0.25 622.84 ±0.42 23.84 ±0.29 25.08 ±0.56 24.49 ±0.62 98.00 ±2.04 22.23 ±0.39 38.11 ±1.19 21.54 ±0.29 22.27 ±0.46 28.90 ±6.09 22.98 ±0.33 30.83 ±5.09 22.35 ±0.47 22.06 ±0.39 24.03 ±0.42 24.72 ±0.43 23.16 ±0.48 25.24 ±0.14 19.84 ±0.70 24.87 ±0.00 22.65 ±0.03 25.77 ±0.00 23.64 ±0.01 28.35 ±0.00 32.03 ±0.80 25.81 ±0.00 23.30 ±0.04 18.64 ±0.79 19.55 ±0.28 1225.62 ±0.41 27.71 ±0.34 27.79 ±0.53 28.42 ±0.62 100.02 ±1.93 25.34 ±0.36 41.47 ±2.03 24.41 ±0.45 25.39 ±0.54 31.36 ±5.41 26.49 ±0.34 36.07 ±4.02 25.35 ±0.62 25.18 ±0.37 26.62 ±0.35 27.54 ±0.47 26.36 ±0.43 30.13 ±0.17 21.03 ±0.61 33.64 ±0.00 28.54 ±0.08 33.36 ±0.00 30.70 ±0.03 36.75 ±0.00 44.91 ±8.74 33.00 ±0.00 29.32 ±0.08 19.85 ±0.76 22.20 ±0.32 Avg 23.29 ±0.43 24.04 ±0.28 25.38 ±0.56 24.84 ±0.65 97.96 ±2.03 22.39 ±0.39 38.29 ±1.20 21.68 ±0.28 22.41 ±0.47 29.03 ±6.07 23.19 ±0.34 31.23 ±4.99 22.53 ±0.49 22.21 ±0.38 24.34 ±0.40 24.97 ±0.45 23.39 ±0.46 25.55 ±0.15 19.88 ±0.68 25.65 ±0.00 23.12 ±0.04 26.22 ±0.00 24.21 ±0.01 28.85 ±0.00 32.90 ±1.12 26.23 ±0.00 23.75 ±0.04 18.66 ±0.79 19.62 ±0.27 MAPE (%) 324.10 ±0.81 21.76 ±0.38 23.21 ±0.43 23.31 ±0.78 79.39 ±1.35 21.38 ±0.30 31.34 ±0.34 20.89 ±0.38 21.45 ±0.51 25.89 ±5.52 23.18 ±0.54 34.95 ±16.21 21.52 ±0.65 21.25 ±0.30 21.75 ±0.39 30.95 ±1.10 22.76 ±0.99 22.34 ±0.37 19.81 ±0.84 19.36 ±0.00 17.99 ±0.04 20.16 ±0.00 18.36 ±0.01 19.80 ±0.00 21.95 ±0.35 19.90 ±0.00 18.89 ±0.01 18.31 ±0.45 18.52 ±0.20 624.33 ±0.75 23.07 ±0.47 23.76 ±0.39 24.42 ±0.81 79.52 ±1.43 22.31 ±0.32 32.02 ±0.39 21.73 ±0.47 22.24 ±0.49 26.69 ±5.49 23.91 ±0.56 36.41 ±15.97 22.36 ±0.64 22.19 ±0.32 22.48 ±0.39 32.23 ±1.07 23.77 ±0.94 24.02 ±0.37 20.23 ±0.87 21.61 ±0.00 19.19 ±0.04 22.53 ±0.00 19.79 ±0.01 22.19 ±0.00 24.49 ±0.32 22.05 ±0.00 20.42 ±0.01 18.75 ±0.46 19.38 ±0.26 1225.99 ±0.73 26.28 ±0.63 25.75 ±0.39 27.32 ±0.86 79.07 ±1.37 24.56 ±0.38 33.58 ±0.89 23.69 ±0.83 24.14 ±0.51 28.62 ±5.53 25.98 ±0.56 39.24 ±15.64 24.53 ±0.73 24.43 ±0.38 24.45 ±0.40 35.38 ±1.06 26.08 ±0.96 28.21 ±0.42 21.03 ±0.84 27.27 ±0.00 21.83 ±0.05 27.51 ±0.00 22.86 ±0.01 26.87 ±0.00 28.81 ±0.24 26.63 ±0.00 23.73 ±0.02 19.61 ±0.46 21.11 ±0.39 Avg 24.66 ±0.77 23.41 ±0.46 24.06 ±0.40 24.76 ±0.81 79.40 ±1.33 22.54 ±0.33 32.16 ±0.38 21.93 ±0.52 22.43 ±0.49 26.88 ±5.50 24.14 ±0.58 36.63 ±16.01 22.60 ±0.66 22.42 ±0.33 22.72 ±0.38 32.58 ±1.07 24.00 ±0.96 24.49 ±0.37 20.28 ±0.85 22.27 ±0.00 19.42 ±0.04 22.96 ±0.00 20.06 ±0.01 22.54 ±0.00 24.70 ±0.29 22.46 ±0.00 20.71 ±0.01 18.80 ±0.45 19.51 ±0.27 PEMS07 MAE 318.59 ±0.29 17.59 ±0.06 19.66 ±0.44 18.38 ±1.08 40.22 ±2.16 16.53 ±0.25 21.47 ±0.50 16.22 ±0.28 16.12 ±0.30 17.90 ±1.53 15.62 ±1.26 17.21 ±0.25 16.37 ±0.15 16.24 ±0.26 18.02 ±0.25 23.09 ±0.91 17.17 ±0.11 17.63 ±0.04 14.67 ±0.34 15.19 ±0.00 14.38 ±0.02 15.97 ±0.00 14.96 ±0.03 18.20 ±0.00 20.28 ±0.24 17.22 ±0.00 14.98 ±0.02 13.00 ±0.06 13.77 ±0.04 618.93 ±0.27 19.22 ±0.05 20.25 ±0.40 19.21 ±0.96 40.32 ±1.94 17.83 ±0.27 22.58 ±0.58 17.53 ±0.32 17.40 ±0.31 19.09 ±1.46 16.93 ±1.25 18.14 ±0.23 17.64 ±0.15 17.55 ±0.27 18.94 ±0.17 24.77 ±1.12 18.44 ±0.08 19.49 ±0.01 15.29 ±0.29 18.03 ±0.00 16.36 ±0.03 19.10 ±0.00 17.51 ±0.02 21.91 ±0.00 23.40 ±0.16 20.19 ±0.00 17.24 ±0.01 13.76 ±0.07 15.12 ±0.06 1221.19 ±0.27 22.81 ±0.08 22.49 ±0.38 21.54 ±0.96 40.46 ±2.10 20.40 ±0.30 24.70 ±0.74 19.94 ±0.36 19.79 ±0.36 21.32 ±1.38 19.34 ±1.26 19.99 ±0.38 20.09 ±0.22 20.14 ±0.30 21.55 ±0.15 28.54 ±1.56 21.02 ±0.10 23.49 ±0.03 16.32 ±0.21 24.47 ±0.00 20.20 ±0.06 25.20 ±0.00 22.33 ±0.02 28.49 ±0.00 29.63 ±0.12 26.07 ±0.00 21.56 ±0.01 14.91 ±0.10 17.46 ±0.09 Avg 19.39 ±0.28 19.56 ±0.05 20.62 ±0.41 19.51 ±0.99 40.30 ±2.05 18.02 ±0.27 22.72 ±0.59 17.67 ±0.31 17.54 ±0.31 19.23 ±1.47 17.07 ±1.26 18.26 ±0.27 17.81 ±0.16 17.74 ±0.27 19.27 ±0.19 25.17 ±1.15 18.64 ±0.09 19.85 ±0.01 15.32 ±0.28 18.67 ±0.00 16.63 ±0.04 19.55 ±0.00 17.86 ±0.02 22.38 ±0.00 23.89 ±0.16 20.58 ±0.00 17.53 ±0.01 13.77 ±0.07 15.22 ±0.06 RMSE 330.83 ±0.32 29.38 ±0.14 36.00 ±0.80 30.15 ±1.49 52.97 ±2.13 27.82 ±0.20 33.25 ±0.58 27.41 ±0.29 27.28 ±0.25 29.96 ±2.69 26.60 ±1.78 28.38 ±0.35 27.62 ±0.15 27.46 ±0.21 29.94 ±0.28 36.09 ±1.22 28.42 ±0.19 29.63 ±0.04 25.56 ±0.32 27.55 ±0.00 26.41 ±0.05 28.60 ±0.00 27.46 ±0.05 32.69 ±0.00 36.91 ±0.74 30.43 ±0.00 27.18 ±0.07 23.51 ±0.08 24.67 ±0.05 631.89 ±0.28 32.54 ±0.12 37.21 ±0.75 31.78 ±1.30 54.08 ±1.79 30.46 ±0.22 35.59 ±0.67 29.94 ±0.33 29.84 ±0.28 32.30 ±2.45 29.14 ±1.82 30.27 ±0.30 30.13 ±0.17 30.10 ±0.22 31.73 ±0.17 38.85 ±1.49 30.90 ±0.16 33.33 ±0.06 26.92 ±0.27 32.91 ±0.00 30.53 ±0.10 34.44 ±0.00 32.80 ±0.03 39.61 ±0.00 42.56 ±0.17 35.69 ±0.00 31.79 ±0.06 25.09 ±0.08 27.21 ±0.09 1236.27 ±0.30 39.02 ±0.14 41.01 ±0.68 35.84 ±1.30 55.87 ±1.97 35.29 ±0.28 39.86 ±0.86 34.34 ±0.39 34.29 ±0.38 36.50 ±2.15 33.55 ±1.93 33.61 ±0.60 34.67 ±0.25 34.96 ±0.28 36.28 ±0.20 45.39 ±2.19 35.56 ±0.17 40.75 ±0.12 28.97 ±0.18 45.31 ±0.00 38.69 ±0.25 46.03 ±0.00 42.92 ±0.05 52.40 ±0.00 59.72 ±6.83 46.50 ±0.00 40.60 ±0.03 27.33 ±0.11 31.28 ±0.14 Avg 32.62 ±0.30 33.05 ±0.13 37.75 ±0.75 32.22 ±1.35 54.10 ±1.93 30.73 ±0.23 35.82 ±0.68 30.13 ±0.32 30.04 ±0.29 32.52 ±2.46 29.33 ±1.84 30.41 ±0.37 30.37 ±0.18 30.37 ±0.23 32.22 ±0.21 39.57 ±1.56 31.19 ±0.17 33.90 ±0.07 26.93 ±0.26 34.18 ±0.00 31.15 ±0.13 35.34 ±0.00 33.57 ±0.03 40.57 ±0.00 44.62 ±1.28 36.42 ±0.00 32.42 ±0.05 25.05 ±0.08 27.30 ±0.08 MAPE (%) 330.48 ±1.24 27.98 ±0.33 31.59 ±1.03 30.73 ±2.59 50.26 ±2.43 26.51 ±1.30 34.13 ±1.18 25.57 ±1.32 25.51 ±2.27 26.75 ±1.59 24.19 ±3.12 27.34 ±0.96 25.71 ±0.67 26.27 ±1.27 32.44 ±0.94 55.33 ±2.34 29.41 ±1.13 27.44 ±0.37 20.97 ±0.86 19.33 ±0.00 18.12 ±0.03 20.30 ±0.00 18.88 ±0.03 20.43 ±0.00 21.13 ±0.06 20.34 ±0.00 18.90 ±0.03 18.51 ±0.27 19.46 ±0.37 630.62 ±1.27 29.47 ±0.24 31.86 ±1.01 31.46 ±2.35 49.24 ±2.48 27.39 ±1.34 34.81 ±1.48 26.44 ±1.29 26.43 ±2.20 27.64 ±1.71 25.38 ±3.00 28.43 ±0.54 26.65 ±0.63 27.16 ±1.32 33.59 ±0.86 58.00 ±2.92 30.46 ±1.12 29.34 ±0.46 21.31 ±0.65 21.88 ±0.00 19.74 ±0.04 23.14 ±0.00 20.91 ±0.02 23.33 ±0.00 24.52 ±0.11 23.12 ±0.00 20.85 ±0.03 18.99 ±0.18 20.67 ±0.39 1232.67 ±1.31 33.46 ±0.27 34.54 ±1.08 33.85 ±2.10 47.91 ±3.13 29.62 ±1.46 36.82 ±2.23 28.63 ±1.18 28.65 ±2.11 29.78 ±1.91 28.11 ±3.10 31.10 ±1.22 28.92 ±0.73 29.40 ±1.43 37.31 ±0.74 64.27 ±4.24 33.08 ±1.16 34.30 ±0.78 22.17 ±0.41 28.40 ±0.00 23.16 ±0.04 29.16 ±0.00 24.96 ±0.02 28.97 ±0.00 29.96 ±0.09 28.69 ±0.00 24.87 ±0.05 20.02 ±0.14 23.20 ±0.40 Avg 31.09 ±1.27 29.95 ±0.26 32.43 ±1.02 31.81 ±2.36 49.24 ±2.54 27.64 ±1.35 35.08 ±1.56 26.68 ±1.27 26.67 ±2.19 27.85 ±1.72 25.66 ±3.04 28.73 ±0.39 26.88 ±0.66 27.40 ±1.33 34.13 ±0.84 58.70 ±3.03 30.76 ±1.13 29.94 ±0.50 21.39 ±0.65 22.66 ±0.00 20.04 ±0.03 23.68 ±0.00 21.24 ±0.02 23.73 ±0.00 24.80 ±0.09 23.57 ±0.00 21.17 ±0.03 19.07 ±0.20 20.90 ±0.39 PEMS08 MAE 314.86 ±0.14 13.63 ±0.05 15.01 ±0.19 14.62 ±0.19 52.44 ±2.51 13.13 ±0.06 16.14 ±0.04 12.76 ±0.09 12.85 ±0.12 14.58 ±0.83 13.32 ±0.44 13.86 ±0.28 12.98 ±0.04 12.95 ±0.06 14.23 ±0.08 17.19 ±0.35 13.42 ±0.09 13.79 ±0.05 11.99 ±0.04 13.26 ±0.00 12.46 ±0.01 13.94 ±0.00 12.77 ±0.02 15.65 ±0.00 17.49 ±0.13 14.90 ±0.00 13.02 ±0.02 11.20 ±0.02 11.87 ±0.03 615.17 ±0.13 14.97 ±0.05 15.60 ±0.16 15.39 ±0.16 52.24 ±2.61 14.18 ±0.07 17.16 ±0.06 13.80 ±0.10 13.91 ±0.12 15.47 ±0.78 14.31 ±0.33 14.66 ±0.28 14.02 ±0.03 14.00 ±0.06 14.83 ±0.06 18.07 ±0.30 14.44 ±0.08 15.28 ±0.04 12.47 ±0.03 15.62 ±0.00 14.00 ±0.02 16.49 ±0.00 14.62 ±0.01 18.77 ±0.00 19.98 ±0.13 17.30 ±0.00 14.75 ±0.02 11.74 ±0.03 12.88 ±0.04 1216.88 ±0.13 17.84 ±0.05 17.43 ±0.16 17.61 ±0.20 52.07 ±3.05 16.27 ±0.09 19.13 ±0.11 15.75 ±0.11 15.90 ±0.17 17.19 ±0.67 16.32 ±0.36 16.25 ±0.27 16.00 ±0.03 16.10 ±0.08 16.83 ±0.06 20.27 ±0.37 16.48 ±0.09 18.53 ±0.04 13.32 ±0.03 21.09 ±0.00 17.01 ±0.04 21.51 ±0.00 18.18 ±0.01 24.43 ±0.00 25.47 ±0.26 22.15 ±0.00 18.10 ±0.03 12.63 ±0.04 14.67 ±0.06 Avg 15.50 ±0.13 15.22 ±0.05 15.86 ±0.17 15.69 ±0.16 52.25 ±2.71 14.34 ±0.07 17.30 ±0.05 13.92 ±0.10 14.04 ±0.13 15.58 ±0.77 14.47 ±0.38 14.76 ±0.28 14.15 ±0.03 14.16 ±0.07 15.12 ±0.07 18.33 ±0.31 14.60 ±0.08 15.58 ±0.04 12.52 ±0.03 16.19 ±0.00 14.22 ±0.02 16.87 ±0.00 14.90 ±0.01 19.21 ±0.00 20.52 ±0.16 17.64 ±0.00 14.99 ±0.02 11.76 ±0.03 12.97 ±0.04 RMSE 323.73 ±0.20 22.36 ±0.08 26.25 ±0.43 23.28 ±0.29 61.63 ±2.94 21.49 ±0.07 24.62 ±0.06 21.01 ±0.12 21.09 ±0.13 23.27 ±1.20 21.64 ±0.51 21.99 ±0.33 21.29 ±0.07 21.26 ±0.05 24.03 ±0.21 26.14 ±0.40 21.79 ±0.12 22.74 ±0.04 19.83 ±0.09 22.30 ±0.00 21.40 ±0.03 23.20 ±0.00 21.87 ±0.03 26.33 ±0.00 29.66 ±0.56 24.72 ±0.00 22.10 ±0.05 18.81 ±0.05 19.93 ±0.04 624.70 ±0.18 24.88 ±0.10 27.48 ±0.38 24.83 ±0.26 62.11 ±3.02 23.63 ±0.09 26.65 ±0.12 23.05 ±0.15 23.19 ±0.16 25.08 ±1.05 23.66 ±0.40 23.65 ±0.34 23.35 ±0.04 23.41 ±0.08 25.24 ±0.16 27.58 ±0.31 23.77 ±0.13 25.65 ±0.03 20.82 ±0.08 26.57 ±0.00 24.61 ±0.06 27.72 ±0.00 25.66 ±0.02 31.97 ±0.00 33.94 ±0.36 28.76 ±0.00 25.56 ±0.05 19.91 ±0.06 21.88 ±0.07 1228.02 ±0.18 29.80 ±0.13 30.67 ±0.37 28.68 ±0.40 63.24 ±3.50 27.52 ±0.13 30.31 ±0.23 26.53 ±0.20 26.81 ±0.29 28.33 ±0.80 27.41 ±0.62 26.49 ±0.45 27.00 ±0.05 27.31 ±0.12 28.72 ±0.14 31.18 ±0.47 27.42 ±0.17 31.37 ±0.05 22.44 ±0.10 36.33 ±0.00 30.88 ±0.15 36.53 ±0.00 32.74 ±0.02 41.51 ±0.00 47.49 ±1.38 37.04 ±0.00 31.97 ±0.08 21.57 ±0.09 25.03 ±0.11 Avg 25.20 ±0.19 25.23 ±0.10 27.85 ±0.40 25.27 ±0.29 62.21 ±3.13 23.85 ±0.09 26.86 ±0.13 23.20 ±0.15 23.35 ±0.18 25.25 ±1.04 23.89 ±0.50 23.76 ±0.37 23.54 ±0.04 23.63 ±0.08 25.69 ±0.17 28.00 ±0.33 23.99 ±0.13 26.07 ±0.04 20.88 ±0.09 27.58 ±0.00 25.08 ±0.08 28.38 ±0.00 26.18 ±0.02 32.55 ±0.00 35.46 ±0.39 29.31 ±0.00 25.97 ±0.06 19.91 ±0.06 21.96 ±0.07 MAPE (%) 322.82 ±0.42 19.07 ±0.41 21.25 ±0.69 20.76 ±0.73 57.52 ±1.13 19.25 ±0.27 22.79 ±0.31 18.05 ±0.22 19.62 ±1.41 21.16 ±1.57 20.30 ±1.59 26.19 ±1.99 18.63 ±0.35 19.13 ±0.27 19.38 ±0.76 41.36 ±1.88 20.82 ±1.06 18.96 ±0.43 17.16 ±0.26 17.01 ±0.00 15.85 ±0.02 17.93 ±0.00 16.36 ±0.01 18.02 ±0.00 18.90 ±0.04 17.86 ±0.00 16.69 ±0.04 16.02 ±0.07 16.31 ±0.10 622.94 ±0.42 20.47 ±0.38 21.71 ±0.71 21.51 ±0.73 56.94 ±1.54 20.33 ±0.24 23.83 ±0.33 19.02 ±0.21 20.70 ±1.34 22.07 ±1.65 21.30 ±1.42 26.35 ±1.97 19.69 ±0.40 20.20 ±0.23 19.98 ±0.75 42.87 ±1.97 21.81 ±1.00 20.66 ±0.40 17.53 ±0.25 19.33 ±0.00 17.22 ±0.03 20.46 ±0.00 17.97 ±0.00 20.63 ±0.00 21.71 ±0.05 20.31 ±0.00 18.33 ±0.04 16.42 ±0.07 17.28 ±0.09 1224.58 ±0.45 23.92 ±0.38 24.00 ±0.73 24.07 ±0.76 56.54 ±2.39 22.74 ±0.27 26.26 ±0.49 21.37 ±0.32 23.18 ±1.24 24.14 ±1.73 23.62 ±0.94 27.80 ±2.10 22.19 ±0.54 22.61 ±0.27 22.15 ±0.79 46.66 ±2.26 24.16 ±0.88 24.95 ±0.43 18.49 ±0.24 25.32 ±0.00 20.17 ±0.04 25.89 ±0.00 21.27 ±0.00 25.69 ±0.00 26.68 ±0.07 25.19 ±0.00 21.82 ±0.04 17.33 ±0.09 19.33 ±0.10 Avg 23.31 ±0.41 20.85 ±0.39 22.13 ±0.71 21.90 ±0.74 57.09 ±1.58 20.58 ±0.25 24.09 ±0.35 19.28 ±0.22 20.96 ±1.33 22.26 ±1.64 21.55 ±1.34 26.61 ±1.73 19.96 ±0.41 20.45 ±0.25 20.33 ±0.76 43.33 ±2.01 22.07 ±0.99 21.16 ±0.42 17.66 ±0.23 20.06 ±0.00 17.49 ±0.03 20.96 ±0.00 18.26 ±0.00 21.00 ±0.00 22.04 ±0.05 20.70 ±0.00 18.63 ±0.04 16.51 ±0.07 17.47 ±0.10 PEMS10 MAE 311.81 ±0.19 11.46 ±0.05 11.82 ±0.09 11.87 ±0.11 81.21 ±3.23 11.09 ±0.04 11.49 ±0.20 10.86 ±0.08 11.14 ±0.06 11.90 ±1.24 11.15 ±0.08 12.84 ±1.70 11.05 ±0.08 11.01 ±0.04 11.85 ±0.09 13.13 ±0.29 11.13 ±0.07 11.73 ±0.04 10.09 ±0.03 11.46 ±0.00 10.79 ±0.01 11.82 ±0.00 11.04 ±0.01 13.03 ±0.00 14.44 ±0.12 12.56 ±0.00 11.24 ±0.00 9.59 ±0.03 10.23 ±0.03 612.06 ±0.14 12.32 ±0.05 12.29 ±0.08 12.38 ±0.11 81.43 ±3.27 11.74 ±0.04 12.23 ±0.23 11.50 ±0.10 11.82 ±0.08 12.51 ±1.18 11.81 ±0.07 13.48 ±1.73 11.68 ±0.09 11.65 ±0.04 12.36 ±0.07 13.62 ±0.32 11.74 ±0.08 12.69 ±0.04 10.32 ±0.03 12.93 ±0.00 11.74 ±0.01 13.38 ±0.00 12.10 ±0.01 15.01 ±0.00 16.15 ±0.13 13.93 ±0.00 12.30 ±0.00 9.84 ±0.03 10.81 ±0.04 1213.19 ±0.15 14.05 ±0.05 13.48 ±0.08 13.70 ±0.14 81.53 ±3.26 13.06 ±0.06 13.70 ±0.29 12.76 ±0.12 13.18 ±0.13 13.72 ±1.04 13.14 ±0.08 14.87 ±1.91 12.97 ±0.10 12.97 ±0.05 13.73 ±0.09 14.81 ±0.35 12.95 ±0.07 14.67 ±0.04 10.73 ±0.04 16.37 ±0.00 13.51 ±0.01 16.49 ±0.00 14.17 ±0.01 18.64 ±0.00 19.70 ±0.22 16.97 ±0.00 14.30 ±0.01 10.26 ±0.03 11.91 ±0.06 Avg 12.26 ±0.16 12.45 ±0.05 12.43 ±0.08 12.54 ±0.11 81.39 ±3.16 11.85 ±0.04 12.35 ±0.23 11.60 ±0.09 11.93 ±0.08 12.61 ±1.16 11.92 ±0.07 13.60 ±1.76 11.79 ±0.09 11.76 ±0.04 12.53 ±0.08 13.75 ±0.32 11.83 ±0.07 12.86 ±0.04 10.34 ±0.03 13.30 ±0.00 11.85 ±0.01 13.63 ±0.00 12.27 ±0.01 15.31 ±0.00 16.45 ±0.14 14.18 ±0.00 12.43 ±0.01 9.86 ±0.03 10.88 ±0.04 RMSE 319.17 ±0.29 19.03 ±0.09 20.39 ±0.16 19.21 ±0.12 83.86 ±3.27 18.21 ±0.02 18.96 ±0.38 17.84 ±0.14 18.31 ±0.08 20.00 ±2.91 18.35 ±0.11 19.71 ±1.41 18.17 ±0.10 18.08 ±0.02 19.33 ±0.09 20.78 ±0.37 18.33 ±0.09 19.35 ±0.05 16.69 ±0.07 19.29 ±0.00 18.45 ±0.03 19.75 ±0.00 18.67 ±0.01 21.83 ±0.00 23.87 ±0.10 20.99 ±0.00 19.00 ±0.02 16.07 ±0.04 17.08 ±0.05 619.79 ±0.24 20.59 ±0.06 21.24 ±0.14 20.20 ±0.12 84.50 ±3.37 19.49 ±0.04 20.39 ±0.45 19.06 ±0.18 19.58 ±0.14 21.13 ±2.71 19.63 ±0.10 20.94 ±1.41 19.40 ±0.10 19.35 ±0.04 20.30 ±0.07 21.60 ±0.41 19.49 ±0.10 21.11 ±0.05 17.17 ±0.05 21.87 ±0.00 20.39 ±0.04 22.48 ±0.00 20.80 ±0.01 25.46 ±0.00 28.17 ±2.25 23.25 ±0.00 21.08 ±0.02 16.57 ±0.03 18.16 ±0.08 1221.96 ±0.25 23.58 ±0.05 23.35 ±0.13 22.52 ±0.20 85.41 ±3.41 21.94 ±0.07 23.10 ±0.55 21.39 ±0.21 22.03 ±0.24 23.31 ±2.32 22.08 ±0.12 23.29 ±1.57 21.80 ±0.14 21.80 ±0.07 22.59 ±0.11 23.56 ±0.44 21.66 ±0.11 24.54 ±0.05 17.96 ±0.05 27.96 ±0.00 24.06 ±0.05 27.93 ±0.00 24.87 ±0.01 32.24 ±0.00 33.91 ±1.29 28.30 ±0.00 24.93 ±0.04 17.36 ±0.03 20.18 ±0.11 Avg 20.13 ±0.26 20.80 ±0.06 21.49 ±0.14 20.45 ±0.13 84.52 ±3.24 19.66 ±0.03 20.58 ±0.45 19.22 ±0.17 19.77 ±0.14 21.29 ±2.68 19.80 ±0.11 21.08 ±1.43 19.58 ±0.10 19.53 ±0.04 20.54 ±0.09 21.81 ±0.40 19.63 ±0.10 21.36 ±0.05 17.20 ±0.05 22.54 ±0.00 20.64 ±0.04 22.92 ±0.00 21.11 ±0.01 25.99 ±0.00 28.09 ±1.21 23.64 ±0.00 21.32 ±0.03 16.58 ±0.03 18.28 ±0.08 MAPE (%) 330.74 ±0.34 28.38 ±0.32 29.73 ±0.29 29.49 ±0.74 756.76 ±29.47 29.11 ±0.29 30.04 ±0.94 28.70 ±0.37 30.52 ±0.75 29.20 ±1.71 29.69 ±0.29 58.30 ±38.83 29.13 ±0.55 28.95 ±0.28 31.70 ±0.31 40.22 ±1.74 29.02 ±0.61 28.77 ±0.41 27.39 ±0.42 27.81 ±0.00 26.36 ±0.07 28.80 ±0.00 27.03 ±0.03 28.16 ±0.00 29.19 ±0.16 28.44 ±0.00 27.36 ±0.03 25.98 ±0.03 26.87 ±0.08 631.29 ±0.33 29.84 ±0.32 30.52 ±0.23 30.31 ±0.69 755.22 ±29.03 30.00 ±0.23 31.38 ±0.98 29.47 ±0.34 31.73 ±0.67 30.11 ±1.70 30.78 ±0.50 58.55 ±40.02 30.04 ±0.59 29.84 ±0.22 32.71 ±0.23 41.21 ±1.76 30.02 ±0.71 30.57 ±0.38 27.74 ±0.45 29.81 ±0.00 27.60 ±0.07 30.98 ±0.00 28.35 ±0.03 30.54 ±0.00 31.69 ±0.10 30.28 ±0.00 28.91 ±0.03 26.34 ±0.05 27.55 ±0.07 1233.45 ±0.41 33.35 ±0.34 32.93 ±0.18 32.78 ±0.66 752.24 ±26.19 32.42 ±0.18 34.68 ±1.59 31.77 ±0.42 35.13 ±0.79 32.53 ±1.65 33.28 ±0.51 62.45 ±42.54 32.43 ±0.61 32.25 ±0.17 35.68 ±0.25 43.96 ±1.88 32.40 ±0.94 34.98 ±0.32 28.55 ±0.44 35.14 ±0.00 30.28 ±0.06 35.86 ±0.00 31.18 ±0.03 35.72 ±0.00 36.23 ±0.13 34.51 ±0.00 32.29 ±0.03 27.08 ±0.07 29.19 ±0.10 Avg 31.65 ±0.35 30.22 ±0.32 30.86 ±0.22 30.65 ±0.69 755.06 ±28.01 30.30 ±0.22 31.79 ±1.11 29.80 ±0.34 32.18 ±0.70 30.41 ±1.69 31.06 ±0.42 59.52 ±40.27 30.34 ±0.58 30.14 ±0.22 33.11 ±0.25 41.57 ±1.79 30.28 ±0.74 31.07 ±0.38 27.83 ±0.45 30.51 ±0.00 27.84 ±0.07 31.47 ±0.00 28.62 ±0.03 30.97 ±0.00 32.02 ±0.11 30.73 ±0.00 29.22 ±0.02 26.41 ±0.04 27.73 ±0.07 PEMS11 MAE 318.69 ±0.36 17.88 ±0.20 20.19 ±0.31 18.90 ±0.41 83.38 ±3.81 17.03 ±0.13 19.74 ±1.56 16.62 ±0.13 16.93 ±0.27 24.48 ±2.64 17.24 ±0.28 23.71 ±3.81 16.91 ±0.12 16.76 ±0.12 18.57 ±0.32 20.18 ±0.43 17.54 ±0.29 18.32 ±0.15 16.33 ±0.16 15.80 ±0.00 14.70 ±0.01 16.84 ±0.00 15.25 ±0.02 18.69 ±0.00 20.45 ±0.14 17.40 ±0.00 15.09 ±0.00 13.40 ±0.06 13.97 ±0.07 619.19 ±0.28 19.63 ±0.17 20.93 ±0.31 19.91 ±0.39 85.10 ±3.52 18.50 ±0.12 21.22 ±1.61 18.07 ±0.12 18.43 ±0.34 25.70 ±2.54 18.77 ±0.21 25.31 ±4.21 18.36 ±0.15 18.26 ±0.12 19.61 ±0.32 21.46 ±0.36 18.98 ±0.29 20.20 ±0.11 16.94 ±0.14 19.21 ±0.00 16.84 ±0.02 20.39 ±0.00 17.88 ±0.02 22.74 ±0.00 24.00 ±0.10 20.82 ±0.00 17.34 ±0.01 14.32 ±0.07 15.44 ±0.08 1221.83 ±0.24 23.48 ±0.12 23.55 ±0.32 22.77 ±0.55 88.77 ±3.23 21.61 ±0.15 24.45 ±1.70 20.92 ±0.13 21.44 ±0.47 28.19 ±2.36 21.86 ±0.16 29.22 ±4.63 21.32 ±0.24 21.38 ±0.15 22.64 ±0.34 24.40 ±0.67 21.99 ±0.27 24.43 ±0.09 18.28 ±0.12 27.09 ±0.00 21.20 ±0.04 27.29 ±0.00 23.15 ±0.03 29.56 ±0.00 30.42 ±0.16 27.38 ±0.00 21.94 ±0.03 15.96 ±0.09 18.12 ±0.10 Avg 19.69 ±0.30 20.00 ±0.16 21.35 ±0.31 20.29 ±0.44 85.43 ±3.52 18.77 ±0.13 21.54 ±1.59 18.29 ±0.13 18.67 ±0.35 25.89 ±2.53 19.02 ±0.23 25.76 ±4.14 18.60 ±0.15 18.52 ±0.13 20.02 ±0.32 21.77 ±0.34 19.24 ±0.28 20.62 ±0.12 17.05 ±0.12 20.04 ±0.00 17.19 ±0.02 20.91 ±0.00 18.32 ±0.02 23.16 ±0.00 24.37 ±0.09 21.24 ±0.00 17.71 ±0.01 14.40 ±0.07 15.60 ±0.08 RMSE 331.04 ±0.45 29.94 ±0.35 37.69 ±0.55 31.36 ±0.74 112.94 ±3.71 28.37 ±0.17 32.65 ±2.94 27.81 ±0.14 28.11 ±0.36 42.15 ±5.33 28.52 ±0.27 37.06 ±5.06 28.19 ±0.16 27.97 ±0.16 30.85 ±0.38 32.56 ±0.56 29.15 ±0.31 30.60 ±0.15 27.05 ±0.36 28.35 ±0.00 26.78 ±0.04 30.08 ±0.00 27.62 ±0.04 33.70 ±0.00 36.68 ±0.41 31.28 ±0.00 27.08 ±0.01 23.33 ±0.09 24.48 ±0.12 632.77 ±0.30 33.71 ±0.26 39.44 ±0.53 33.73 ±0.69 116.32 ±3.41 31.76 ±0.14 35.91 ±2.87 31.05 ±0.11 31.50 ±0.44 44.47 ±4.94 31.98 ±0.20 40.37 ±5.70 31.47 ±0.20 31.38 ±0.13 33.20 ±0.37 35.12 ±0.52 32.37 ±0.31 34.80 ±0.12 28.65 ±0.25 35.45 ±0.00 31.71 ±0.06 37.19 ±0.00 33.61 ±0.08 41.63 ±0.00 43.90 ±0.27 37.82 ±0.00 32.06 ±0.04 25.63 ±0.10 27.84 ±0.12 1238.65 ±0.27 41.33 ±0.17 44.47 ±0.51 39.49 ±1.05 123.41 ±3.10 38.27 ±0.17 42.48 ±2.88 36.98 ±0.16 37.79 ±0.69 49.10 ±4.27 38.39 ±0.19 47.69 ±6.19 37.68 ±0.32 37.94 ±0.17 39.19 ±0.37 40.62 ±1.15 38.55 ±0.30 43.44 ±0.13 31.70 ±0.19 51.41 ±0.00 41.40 ±0.19 50.75 ±0.00 44.93 ±0.10 54.25 ±0.00 56.11 ±0.11 50.35 ±0.00 41.93 ±0.10 29.38 ±0.12 33.49 ±0.16 Avg 33.66 ±0.34 34.32 ±0.27 40.11 ±0.53 34.35 ±0.80 116.95 ±3.38 32.21 ±0.15 36.45 ±2.86 31.40 ±0.13 31.90 ±0.47 44.81 ±4.91 32.38 ±0.23 41.08 ±5.52 31.88 ±0.20 31.83 ±0.15 33.89 ±0.36 35.62 ±0.53 32.79 ±0.31 35.52 ±0.13 28.82 ±0.20 37.05 ±0.00 32.41 ±0.08 38.14 ±0.00 34.43 ±0.07 42.24 ±0.00 44.37 ±0.19 38.56 ±0.00 32.78 ±0.04 25.74 ±0.10 28.06 ±0.13 MAPE (%) 330.78 ±0.93 24.39 ±0.34 29.45 ±0.64 26.32 ±0.78 77.32 ±15.78 26.11 ±0.80 28.92 ±0.90 23.82 ±0.70 26.53 ±1.24 35.21 ±6.88 28.98 ±1.96 45.25 ±14.22 27.10 ±0.83 25.97 ±0.79 30.64 ±1.81 45.43 ±2.56 29.58 ±2.86 24.98 ±0.73 23.94 ±0.63 21.66 ±0.00 20.03 ±0.04 22.80 ±0.00 20.81 ±0.03 22.44 ±0.00 23.02 ±0.01 22.43 ±0.00 20.95 ±0.01 20.75 ±0.22 22.48 ±0.39 630.74 ±0.87 26.12 ±0.37 29.65 ±0.33 27.14 ±0.80 80.97 ±18.12 27.25 ±0.78 30.36 ±1.20 25.01 ±0.79 27.76 ±1.43 36.53 ±6.71 30.24 ±1.63 46.71 ±12.65 28.41 ±1.01 27.11 ±0.78 31.58 ±1.76 47.41 ±2.67 30.58 ±2.79 26.94 ±0.61 24.36 ±0.69 24.49 ±0.00 21.62 ±0.04 25.85 ±0.00 22.74 ±0.04 25.41 ±0.00 26.42 ±0.04 25.28 ±0.00 22.88 ±0.02 21.31 ±0.25 23.52 ±0.39 1232.84 ±0.78 30.75 ±0.53 32.76 ±0.27 29.87 ±0.87 89.84 ±23.97 30.48 ±0.87 34.14 ±1.85 28.09 ±0.80 31.40 ±2.51 39.89 ±6.43 33.90 ±1.15 51.27 ±11.76 31.92 ±1.30 30.33 ±0.87 35.10 ±1.52 52.32 ±3.03 33.38 ±2.70 32.38 ±0.59 25.71 ±0.78 31.70 ±0.00 25.05 ±0.03 32.22 ±0.00 26.79 ±0.04 30.99 ±0.00 31.71 ±0.03 31.06 ±0.00 26.96 ±0.05 22.59 ±0.30 25.80 ±0.38 Avg 31.28 ±0.86 26.69 ±0.39 30.37 ±0.32 27.55 ±0.81 82.12 ±18.72 27.67 ±0.81 30.83 ±1.25 25.39 ±0.75 28.29 ±1.63 36.90 ±6.66 30.78 ±1.62 47.34 ±12.72 28.85 ±1.00 27.53 ±0.80 32.17 ±1.75 48.00 ±2.68 30.95 ±2.77 27.66 ±0.61 24.54 ±0.69 25.36 ±0.00 21.93 ±0.04 26.41 ±0.00 23.11 ±0.03 25.78 ±0.00 26.67 ±0.03 25.78 ±0.00 23.23 ±0.03 21.44 ±0.25 23.73 ±0.38 Conference’17, July 2017, Washington, DC, USAYin et al. Table 6: Per-horizon results on PEMS12 and TFNSW (mean±SD). Static STGNN BackbonesNaïve SchemesEvolving GraphRetrieval TTCStatic Forecasting BackbonesTSFMsOurs Metric Len DCRNN ASTGNN TGCNGWNPretrain Retrain OL-N OL-AN TrafStm PECPM STKECEACSTRAP ST-TTCSTIDSTNorm iTrans DLinear STAE Chro2-Z Chro2-F TimesF-Z TimesF-T Moira1-Z Moira1-T Moira2-Z Moira2-T A2TTA-S A2TTA-O PEMS12 MAE 315.43 ±0.22 14.23 ±0.12 16.26 ±0.09 15.16 ±0.28 15.17 ±0.18 13.59 ±0.05 16.25 ±0.47 13.24 ±0.05 13.42 ±0.06 14.97 ±1.63 13.42 ±0.10 13.96 ±0.25 13.59 ±0.15 13.41 ±0.05 15.00 ±0.09 17.97 ±0.53 13.92 ±0.13 14.31 ±0.02 12.39 ±0.11 13.51 ±0.00 12.73 ±0.00 14.31 ±0.00 13.24 ±0.03 15.91 ±0.00 17.32 ±0.62 14.88 ±0.00 13.21 ±0.01 11.37 ±0.04 12.11 ±0.02 615.76 ±0.16 15.67 ±0.09 16.80 ±0.08 16.11 ±0.25 16.28 ±0.20 14.75 ±0.05 17.78 ±0.56 14.40 ±0.06 14.60 ±0.06 16.02 ±1.50 14.57 ±0.08 14.84 ±0.28 14.72 ±0.14 14.57 ±0.05 15.76 ±0.07 19.17 ±0.41 15.06 ±0.10 15.90 ±0.02 12.87 ±0.10 16.05 ±0.00 14.41 ±0.01 17.06 ±0.00 15.37 ±0.03 19.07 ±0.00 20.17 ±0.58 17.51 ±0.00 15.06 ±0.01 11.94 ±0.05 13.20 ±0.01 1217.77 ±0.14 18.87 ±0.10 18.83 ±0.06 18.46 ±0.20 18.34 ±0.30 17.02 ±0.06 20.91 ±0.77 16.58 ±0.09 16.81 ±0.13 18.11 ±1.30 16.75 ±0.10 16.63 ±0.44 16.95 ±0.14 16.87 ±0.07 18.07 ±0.06 22.03 ±0.30 17.48 ±0.08 19.37 ±0.03 13.70 ±0.12 21.94 ±0.00 17.73 ±0.04 22.48 ±0.00 19.51 ±0.03 24.73 ±0.00 25.32 ±0.63 22.80 ±0.00 18.67 ±0.01 12.81 ±0.07 15.09 ±0.02 Avg16.16 ±0.17 15.98 ±0.10 17.13 ±0.08 16.38 ±0.23 16.41 ±0.21 14.91 ±0.05 18.04 ±0.57 14.54 ±0.06 14.74 ±0.07 16.18 ±1.49 14.71 ±0.08 14.98 ±0.30 14.88 ±0.14 14.74 ±0.05 16.07 ±0.07 19.49 ±0.39 15.27 ±0.11 16.23 ±0.02 12.91 ±0.11 16.67 ±0.00 14.66 ±0.01 17.48 ±0.00 15.69 ±0.02 19.49 ±0.00 20.49 ±0.59 17.90 ±0.00 15.32 ±0.01 11.95 ±0.05 13.28 ±0.01 RMSE 326.80 ±0.31 25.07 ±0.18 31.84 ±0.21 26.13 ±0.45 25.43 ±0.16 23.87 ±0.08 28.37 ±0.92 23.41 ±0.03 23.68 ±0.09 26.16 ±3.54 23.69 ±0.15 24.14 ±0.31 23.87 ±0.18 23.58 ±0.05 26.16 ±0.22 29.50 ±0.83 24.26 ±0.18 25.36 ±0.03 22.03 ±0.12 24.46 ±0.00 23.44 ±0.02 25.67 ±0.00 24.31 ±0.05 29.08 ±0.00 32.10 ±1.13 26.66 ±0.00 24.10 ±0.03 20.53 ±0.06 21.80 ±0.03 627.76 ±0.23 28.00 ±0.16 32.92 ±0.19 28.03 ±0.39 27.77 ±0.22 26.29 ±0.06 31.54 ±1.11 25.78 ±0.06 26.12 ±0.09 28.34 ±3.19 26.08 ±0.12 26.01 ±0.36 26.23 ±0.17 26.03 ±0.04 27.64 ±0.19 31.61 ±0.57 26.59 ±0.14 28.70 ±0.05 23.09 ±0.11 29.57 ±0.00 27.08 ±0.04 31.07 ±0.00 29.01 ±0.05 35.26 ±0.00 37.46 ±1.02 31.59 ±0.00 28.07 ±0.03 21.73 ±0.07 23.97 ±0.02 1231.86 ±0.20 34.05 ±0.23 36.42 ±0.17 32.38 ±0.27 31.84 ±0.41 30.73 ±0.07 37.79 ±1.53 29.93 ±0.15 30.40 ±0.22 32.39 ±2.68 30.26 ±0.19 29.33 ±0.71 30.58 ±0.21 30.50 ±0.08 31.73 ±0.20 36.73 ±0.45 31.16 ±0.13 35.51 ±0.08 24.77 ±0.15 41.53 ±0.00 34.49 ±0.19 41.80 ±0.00 38.08 ±0.07 46.15 ±0.00 47.62 ±0.88 41.70 ±0.00 35.73 ±0.01 23.45 ±0.11 27.45 ±0.05 Avg28.46 ±0.25 28.49 ±0.18 33.43 ±0.19 28.47 ±0.35 27.96 ±0.24 26.54 ±0.06 32.01 ±1.14 25.97 ±0.07 26.32 ±0.10 28.57 ±3.19 26.28 ±0.12 26.18 ±0.40 26.48 ±0.17 26.28 ±0.05 28.14 ±0.19 32.19 ±0.51 26.92 ±0.15 29.24 ±0.05 23.13 ±0.12 30.85 ±0.00 27.68 ±0.07 31.92 ±0.00 29.74 ±0.05 36.00 ±0.00 38.04 ±1.02 32.32 ±0.00 28.62 ±0.02 21.71 ±0.08 24.05 ±0.02 MAPE (%) 330.24 ±0.93 24.84 ±0.51 29.71 ±0.50 25.72 ±0.40 27.23 ±0.80 25.35 ±0.64 27.74 ±0.49 24.09 ±0.35 25.52 ±0.76 28.04 ±1.67 24.99 ±0.83 28.88 ±3.23 25.59 ±1.28 25.24 ±0.63 31.60 ±0.74 55.15 ±2.04 27.92 ±1.57 24.78 ±0.36 23.40 ±0.78 22.43 ±0.00 20.71 ±0.03 23.78 ±0.00 21.67 ±0.02 23.72 ±0.00 24.09 ±0.26 23.33 ±0.00 21.79 ±0.02 21.39 ±0.23 21.95 ±0.18 630.30 ±0.77 26.69 ±0.51 29.80 ±0.42 26.82 ±0.39 28.24 ±0.93 26.56 ±0.55 29.07 ±0.52 25.13 ±0.23 26.46 ±0.63 29.04 ±1.40 26.32 ±0.61 29.31 ±2.63 26.69 ±1.16 26.45 ±0.53 33.05 ±0.86 58.10 ±2.24 28.96 ±1.38 27.01 ±0.44 23.81 ±0.72 25.58 ±0.00 22.46 ±0.04 27.22 ±0.00 23.88 ±0.03 27.23 ±0.00 28.45 ±0.18 26.61 ±0.00 23.97 ±0.02 21.87 ±0.24 23.15 ±0.12 1232.77 ±0.67 31.71 ±0.65 33.40 ±0.39 30.26 ±0.53 30.60 ±1.19 29.49 ±0.46 32.30 ±0.73 27.98 ±0.40 29.56 ±0.75 31.53 ±0.96 29.50 ±0.47 31.58 ±2.32 29.76 ±1.26 29.39 ±0.45 37.84 ±1.06 65.26 ±2.85 31.77 ±1.26 32.90 ±0.72 24.90 ±0.70 33.94 ±0.00 26.38 ±0.07 34.72 ±0.00 28.54 ±0.03 34.24 ±0.00 35.19 ±0.14 33.62 ±0.00 28.62 ±0.03 22.95 ±0.23 25.61 ±0.11 Avg30.90 ±0.78 27.32 ±0.53 30.68 ±0.38 27.32 ±0.41 28.48 ±0.81 26.88 ±0.52 29.42 ±0.55 25.48 ±0.28 26.88 ±0.62 29.30 ±1.38 26.66 ±0.60 29.71 ±2.65 27.09 ±1.22 26.77 ±0.51 33.77 ±0.88 58.93 ±2.28 29.32 ±1.41 27.74 ±0.47 23.94 ±0.74 26.63 ±0.00 22.84 ±0.04 27.93 ±0.00 24.31 ±0.02 27.76 ±0.00 28.81 ±0.19 27.26 ±0.00 24.38 ±0.02 21.98 ±0.24 23.36 ±0.11 TFNSW MAE 3168.71 ±15.14 122.66 ±1.26 195.29 ±1.44 143.12 ±2.43 257.73 ±11.31 120.27 ±0.46 148.65 ±3.87 114.38 ±1.09 126.95 ±2.36 160.08 ±23.60 129.61 ±0.97 124.47 ±2.51 118.46 ±1.42 129.39 ±0.47 146.99 ±8.64 132.28 ±2.29 127.68 ±0.63 155.32 ±0.84 88.89 ±1.68 160.32 ±0.00 128.86 ±0.38 190.66 ±0.00 165.69 ±0.60 255.65 ±0.00 288.08 ±1.27 204.29 ±0.00 114.89 ±0.23 61.18 ±0.30 76.26 ±0.21 6181.43 ±14.38 145.13 ±0.79 211.00 ±1.58 175.19 ±3.28 261.85 ±11.96 142.34 ±0.66 180.04 ±3.54 134.84 ±1.26 150.05 ±2.33 177.30 ±21.89 152.15 ±1.41 139.81 ±1.76 139.74 ±2.06 147.98 ±0.77 151.13 ±5.35 150.92 ±2.57 148.02 ±0.71 191.54 ±1.27 95.46 ±1.73 245.53 ±0.00 171.51 ±0.85 282.31 ±0.00 234.82 ±0.32 324.03 ±0.00 362.17 ±0.58 301.81 ±0.00 151.95 ±0.30 68.18 ±0.34 88.38 ±0.24 12191.66 ±13.98 158.22 ±0.48 219.72 ±1.46 203.53 ±4.54 269.70 ±12.03 156.34 ±0.69 199.28 ±4.63 148.00 ±1.26 164.32 ±2.37 189.11 ±20.37 167.11 ±1.75 154.35 ±1.24 153.70 ±2.03 160.78 ±0.84 162.81 ±4.96 170.66 ±2.26 161.09 ±1.47 205.55 ±1.20 107.50 ±1.60 288.66 ±0.00 187.39 ±0.77 345.79 ±0.00 256.73 ±0.39 359.26 ±0.00 371.62 ±0.68 399.37 ±0.00 167.54 ±0.34 78.02 ±0.42 101.46 ±0.59 Avg 179.87 ±14.50 140.15 ±0.82 208.33 ±1.48 170.89 ±3.29 262.63 ±10.87 138.04 ±0.62 174.36 ±3.31 130.61 ±0.96 145.42 ±2.41 174.19 ±22.07 147.86 ±1.05 137.90 ±1.42 135.57 ±1.80 144.41 ±0.72 153.63 ±6.20 148.78 ±2.33 144.04 ±0.82 182.20 ±1.03 96.12 ±1.67 227.74 ±0.00 160.20 ±0.68 266.77 ±0.00 215.22 ±0.33 306.03 ±0.00 334.59 ±0.89 294.05 ±0.00 142.36 ±0.28 67.89 ±0.32 86.78 ±0.24 RMSE 3280.25 ±20.45 217.63 ±1.09 371.81 ±3.45 262.49 ±4.16 370.25 ±14.96 215.03 ±0.78 269.38 ±4.49 205.28 ±2.18 224.54 ±4.17 292.97 ±49.14 224.34 ±1.36 219.33 ±3.97 211.67 ±3.60 229.39 ±0.90 291.53 ±13.80 241.64 ±3.36 226.79 ±1.65 277.14 ±1.12 171.62 ±2.96 327.55 ±0.00 268.64 ±1.59 369.29 ±0.00 336.90 ±0.43 462.40 ±0.00 561.94 ±2.60 417.01 ±0.00 252.28 ±0.75 129.32 ±0.65 154.06 ±0.79 6308.03 ±18.86 256.45 ±1.03 394.80 ±3.35 326.67 ±6.57 384.60 ±12.76 257.56 ±1.26 333.40 ±6.29 244.87 ±2.33 270.67 ±4.71 326.33 ±44.92 271.09 ±2.95 250.85 ±2.25 253.32 ±4.77 265.94 ±1.21 303.05 ±8.85 280.63 ±3.49 266.95 ±2.18 335.83 ±1.27 189.36 ±3.02 473.73 ±0.00 348.32 ±2.49 519.48 ±0.00 458.77 ±1.05 570.16 ±0.00 649.78 ±1.17 565.48 ±0.00 326.33 ±0.66 147.94 ±0.81 180.12 ±0.90 12327.96 ±18.20 282.09 ±0.90 407.82 ±2.97 370.26 ±8.00 402.93 ±11.34 283.78 ±1.17 365.29 ±9.55 269.48 ±2.24 296.76 ±4.74 346.80 ±41.06 297.74 ±2.86 277.73 ±1.60 279.24 ±4.41 290.96 ±1.24 330.87 ±7.88 318.01 ±2.67 290.09 ±2.68 358.40 ±1.12 219.12 ±2.63 546.05 ±0.00 372.36 ±2.11 608.15 ±0.00 493.26 ±0.47 648.32 ±0.00 652.88 ±0.85 692.51 ±0.00 352.26 ±0.80 173.98 ±0.61 211.44 ±1.27 Avg 303.16 ±19.20 247.22 ±1.02 390.75 ±3.25 313.61 ±5.86 383.38 ±12.29 247.58 ±1.00 318.17 ±5.87 235.35 ±1.95 259.40 ±4.67 318.61 ±45.67 259.82 ±2.21 245.35 ±1.93 243.47 ±4.15 257.96 ±1.08 307.19 ±10.11 275.25 ±3.16 257.27 ±2.16 318.13 ±1.10 190.33 ±2.83 440.18 ±0.00 323.47 ±2.06 487.06 ±0.00 420.65 ±0.52 544.51 ±0.00 609.59 ±1.67 545.09 ±0.00 303.78 ±0.69 147.15 ±0.64 176.97 ±0.84 MAPE (%) 3203.98 ±42.96 101.54 ±2.40 167.79 ±4.05 109.87 ±6.56 419.02 ±18.83 93.75 ±3.87 121.57 ±11.39 87.14 ±5.01 94.78 ±7.81 94.19 ±7.03 134.83 ±7.19 109.08 ±12.15 93.03 ±3.88 99.28 ±3.48 112.69 ±14.09 162.98 ±5.57 98.77 ±5.85 154.16 ±5.94 59.94 ±3.07 60.65 ±0.00 54.11 ±0.13 84.30 ±0.00 73.71 ±1.57 103.01 ±0.00 54.54 ±0.87 68.13 ±0.00 43.39 ±0.01 49.30 ±0.51 56.66 ±1.98 6210.50 ±43.26 130.32 ±3.10 176.75 ±3.86 137.59 ±9.85 427.56 ±35.35 104.87 ±3.92 131.86 ±9.09 102.09 ±3.95 108.40 ±8.04 108.65 ±5.53 147.27 ±10.71 122.40 ±16.15 105.70 ±3.72 106.79 ±3.16 110.90 ±12.12 183.80 ±8.11 114.90 ±9.27 194.19 ±6.66 64.60 ±2.35 117.43 ±0.00 82.43 ±0.32 163.00 ±0.00 128.42 ±0.85 164.37 ±0.00 164.10 ±1.19 131.57 ±0.00 65.49 ±0.27 53.55 ±0.32 66.51 ±1.39 12221.79 ±41.52 146.31 ±4.51 188.49 ±3.75 174.63 ±17.60 438.74 ±48.59 115.98 ±3.12 137.54 ±6.98 114.71 ±2.98 120.47 ±9.27 119.62 ±3.65 162.82 ±10.53 132.49 ±17.32 117.09 ±2.11 115.50 ±2.33 111.46 ±8.46 206.11 ±5.57 130.80 ±6.23 218.83 ±4.82 76.98 ±1.65 182.97 ±0.00 99.59 ±0.44 242.48 ±0.00 171.51 ±0.37 207.96 ±0.00 206.18 ±1.08 226.64 ±0.00 80.90 ±0.33 63.01 ±0.27 77.64 ±1.30 Avg 211.72 ±42.72 125.28 ±3.02 177.95 ±3.89 138.49 ±10.57 430.83 ±35.95 104.00 ±3.59 129.82 ±8.24 99.93 ±3.54 106.92 ±8.01 106.24 ±4.44 148.01 ±7.69 119.37 ±14.85 104.21 ±3.09 106.33 ±3.01 112.25 ±11.68 182.00 ±6.10 113.97 ±6.78 187.17 ±5.55 66.43 ±2.35 120.67 ±0.00 78.26 ±0.28 160.45 ±0.00 124.25 ±0.83 155.80 ±0.00 144.74 ±1.00 137.97 ±0.00 62.69 ±0.22 54.66 ±0.33 66.01 ±1.49 Newly added sensors. Figure 13 isolates nodes added at graph- growing transitions. A 2 TTA(STAE) is best in all 360 plotted com- binations and reduces MAE, RMSE, and MAPE relative to frozen STAEFormer by 9.1%, 7.4%, and 8.8% on average, respectively. Average-horizon baseline comparison. While the per-step plot focuses on six representative methods, Figures 7 and 14 broadens the Avg comparison to the full baseline set. Together, the figures cover all nine EvoXXLTraffic districts and TFNSW. A 2 TTA(STAE) ranks first in 29 of the 30 comparable panels. The only excep- tion is TFNSW RMSE, where A 2 TTA(OLAN) records 177.20 and A 2 TTA(STAE) records 178.38. Averaged equally across datasets, A 2 TTA(STAE) reduces MAE, RMSE, and MAPE by 10.2%, 8.3%, and 9.2% relative to frozen STAEFormer, and by 8.8%, 8.1%, and 7.0% relative to A 2 TTA(OLAN). Its MAE reduction over frozen STAE- Former ranges from 4.2% on PEMS10 to 33.7% on TFNSW, including 12.6% on PEMS04 and 9.9% on PEMS11. Daggered TSFM-FT bars are all-sensor references and are excluded from these new-sensor rankings. A.4 Drift-Severity Analysis Details Metrics and aggregation. This auxiliary diagnostic uses legacy batched outputs. It joins drift measurements to paired yearly er- rors from the five-seed analysis and to one pre-specified seed for the all-network breadth check. For consecutive years푦 −1 and푦, traffic-distribution drift is the 1-Wasserstein distance be- tween deterministic samples of the two raw traffic arrays, nor- malized by their average standard deviation. Graph-density drift is| log(훿 푦 /훿 푦−1 )|, where훿 푦 is the nonzero adjacency density. For TFNSW, sensor churn is computed from exact yearly sensor IDs as(|V 푦 \ V 푦−1 | + |V 푦−1 \ V 푦 |)/|V 푦 ∪ V 푦−1 |. The correspond- ing PEMS analysis uses the conservative net-count lower bound |푁 푦 − 푁 푦−1 |/max(푁 푦 ,푁 푦−1 ), because the processed experimental arrays used for this diagnostic do not retain the full station-ID transition record. For a backbone푏, the relative gain in dataset푑and year푦is 100(MAE 푏,푑,푦 −MAE A 2 TTA(푏),푑,푦 )/MAE 푏,푑,푦 . The primary layer first averages the errors within each dataset-year over the five paired seeds and contains 47 Online-AN and 87 STAEFormer yearly cells. Quartiles are formed separately for each backbone and drift signal. Their intervals are nonparametric 95% bootstrap intervals over the resulting yearly cells, rather than seed-level intervals. The breadth layer uses one pre-specified seed and covers 223 adjacent-year cells per backbone across all ten networks. It is a breadth check rather than an additional inference layer and therefore has no error bars. Detailed observations. Full A 2 TTA improves every yearly cell in the paired five-seed layer, so all primary quartile means and confidence intervals in Figure 15 remain above zero. Normalized Wasserstein drift has no reliable monotonic association with gain (휌=0.163,푝= .275 for Online-AN and휌=0.123,푝= .255 for STAEFormer). The gain remains positive across the observed sever- ity range. Structural drift is more informative. For STAEFormer, graph-density change is positively associated with gain (휌=0.228, 푝= .034), while sensor churn gives휌=0.209 (푝= .052). The pri- mary Online-AN churn association is weaker, but its highest-churn quartile still has the largest mean gain (9.0%). In the all-network breadth layer, churn is positively associated with gain for both Online-AN (휌=0.263) and STAEFormer (휌=0.241), with both 푝< .001. The highest-churn quartile reaches 13.5% and 11.4%, respectively. These diagnostics show positive gains across the ob- served temporal shifts and a larger benefit during severe sensor turnover. A.5 Long-Term Adaptation Breadth This legacy-batched, pre-specified single-seed check covers ten datasets (fig. 16). Mean MAE improvements over frozen backbones range from 3.7% to 26.8%. The figure also reports yearly win rates against global-only TTA and the corresponding backbone. Timing repeats are not independent seeds. A.6 Protocol Controls and Deployment Cost Protocol checks. The result files behind every main-table A 2 TTA cell record an evaluation batch size of one, training-only input nor- malization, metadata-based sensor identities, a 12-step label delay, and a 64-window global-update interval. The matched backbone row uses the same per-year checkpoint and seed. For the new- sensor comparison, all 21 comparable methods were evaluated on the same metadata-defined transition cohorts over ten networks and five seeds. Dependence on yearly warm-up. We also initialize the FiLM cali- brator as the identity and skip its three warm-up epochs on PEMS05, PEMS08, and TFNSW. Across five paired seeds, removing warm-up A 2 TTA: Anchored-and-Agile Test-Time Adaptation for Evolving Traffic Sensor NetworksConference’17, July 2017, Washington, DC, USA 123456789101112 Horizon 10.0 12.5 15.0 17.5 20.0 22.5 25.0 MAE 123456789101112 Horizon 20 25 30 35 40 RMSE 123456789101112 Horizon 20 25 30 35 40 45 50 MAPE (%) 123456789101112 Horizon 15 20 25 30 35 40 MAE 123456789101112 Horizon 30 40 50 60 RMSE 123456789101112 Horizon 15 20 25 30 35 40 MAPE (%) 123456789101112 Horizon 10 12 14 16 MAE 123456789101112 Horizon 14 16 18 20 22 24 26 RMSE 123456789101112 Horizon 20 25 30 35 40 45 50 MAPE (%) 123456789101112 Horizon 12.5 15.0 17.5 20.0 22.5 25.0 MAE 123456789101112 Horizon 20 25 30 35 40 RMSE 123456789101112 Horizon 20 25 30 35 40 MAPE (%) 123456789101112 Horizon 15 20 25 30 35 MAE 123456789101112 Horizon 30 40 50 60 RMSE 123456789101112 Horizon 20 40 60 80 MAPE (%) 123456789101112 Horizon 12 14 16 18 20 22 MAE 123456789101112 Horizon 17.5 20.0 22.5 25.0 27.5 30.0 32.5 35.0 RMSE 123456789101112 Horizon 15 20 25 30 35 40 45 50 MAPE (%) 123456789101112 Horizon 10 12 14 16 18 MAE 123456789101112 Horizon 16 18 20 22 24 26 28 RMSE 123456789101112 Horizon 25 30 35 40 45 50 55 60 MAPE (%) 123456789101112 Horizon 15 20 25 30 MAE 123456789101112 Horizon 20 25 30 35 40 45 50 55 RMSE 123456789101112 Horizon 20 30 40 50 60 MAPE (%) 123456789101112 Horizon 12.5 15.0 17.5 20.0 22.5 25.0 MAE 123456789101112 Horizon 20 25 30 35 40 RMSE 123456789101112 Horizon 20 30 40 50 60 70 MAPE (%) 123456789101112 Horizon 50 100 150 200 250 MAE 123456789101112 Horizon 100 150 200 250 300 350 400 450 RMSE 123456789101112 Horizon 50 100 150 200 250 MAPE (%) (a) PEMS03(b) PEMS04 (c) PEMS05(d) PEMS06 (e) PEMS07(f) PEMS08 (g) PEMS10(h) PEMS11 (i) PEMS12(j) TFNSW A2TTA(STAE)STAEFormerST-TTCEACGWNSTNorm Figure 12: All-sensor per-step results on ten networks. increases Avg-MAE by 1.0%, 1.1%, and 2.4% for the STAEFormer variant and by 1.7%, 1.4%, and 11.4% for the Online-AN variant, respectively. A 2 TTA can therefore enter the causal stream with- out calibrator warm-up, but the labeled training partition provides a measurable and sometimes substantial benefit. We retain three warm-up epochs in the main protocol and do not present it as label-free deployment. Controlled cost measurement. We profile the frozen backbone, warm-up-only calibration, global-only TTA, and full A 2 TTA on one H200 GPU over 233 natural yearly graph snapshots. Each snap- shot is repeated three times before aggregation. Full A 2 TTA av- erages 5.35 ms per window with Online-AN and 11.60 ms with STAEFormer; the frozen backbones require 4.30 and 10.48 ms, re- spectively. For STAEFormer, peak allocated GPU memory rises from 10,021 to 10,552 MiB. The calibrator has an average of 33.2K Conference’17, July 2017, Washington, DC, USAYin et al. 123456789101112 Horizon 8 10 12 14 16 18 MAE 123456789101112 Horizon 15 20 25 30 RMSE 123456789101112 Horizon 30 40 50 60 MAPE (%) 123456789101112 Horizon 15 20 25 30 35 40 MAE 123456789101112 Horizon 20 30 40 50 60 RMSE 123456789101112 Horizon 15 20 25 30 35 40 45 50 MAPE (%) 123456789101112 Horizon 8 10 12 14 16 18 MAE 123456789101112 Horizon 12 14 16 18 20 22 24 26 RMSE 123456789101112 Horizon 30 40 50 60 70 80 MAPE (%) 123456789101112 Horizon 10.0 12.5 15.0 17.5 20.0 22.5 25.0 MAE 123456789101112 Horizon 15 20 25 30 35 RMSE 123456789101112 Horizon 20 25 30 35 40 MAPE (%) 123456789101112 Horizon 10 15 20 25 30 35 MAE 123456789101112 Horizon 20 25 30 35 40 45 50 55 RMSE 123456789101112 Horizon 20 30 40 50 60 MAPE (%) 123456789101112 Horizon 10 12 14 16 18 20 22 24 MAE 123456789101112 Horizon 20 25 30 35 RMSE 123456789101112 Horizon 20 30 40 50 MAPE (%) 123456789101112 Horizon 8 10 12 14 MAE 123456789101112 Horizon 12 14 16 18 20 22 RMSE 123456789101112 Horizon 30 40 50 60 70 80 90 MAPE (%) 123456789101112 Horizon 15 20 25 30 35 MAE 123456789101112 Horizon 20 25 30 35 40 45 50 55 RMSE 123456789101112 Horizon 20 30 40 50 MAPE (%) 123456789101112 Horizon 10.0 12.5 15.0 17.5 20.0 22.5 25.0 MAE 123456789101112 Horizon 20 25 30 35 40 RMSE 123456789101112 Horizon 20 30 40 50 60 MAPE (%) 123456789101112 Horizon 100 150 200 250 MAE 123456789101112 Horizon 150 200 250 300 350 400 450 500 RMSE 123456789101112 Horizon 50 100 150 200 250 300 350 400 MAPE (%) (a) PEMS03(b) PEMS04 (c) PEMS05(d) PEMS06 (e) PEMS07(f) PEMS08 (g) PEMS10(h) PEMS11 (i) PEMS12(j) TFNSW A2TTA(STAE)STAEFormerST-TTCEACGWNSTNorm Figure 13: New-sensor per-step results on ten networks. updated parameters, including the node table, equal to 1.6% of the 2.06M-parameter STAEFormer backbone. Yearly online adaptation averages 2.1 s for Online-AN and 2.0 s for STAEFormer after warm- up. A.7 Hyperparameter Sensitivity The Online-AN variant uses 3×10 −3 on PEMS03, PEMS04, PEMS06, PEMS11, and TFNSW and 10 −3 elsewhere. The STAEFormer variant uses 3× 10 −3 on TFNSW and 10 −3 elsewhere. Figure 17 reports a one-at-a-time singleton-window sweep on PEMS03, PEMS05, and PEMS06 with seeds 51 to 53. The non- learning-rate defaults are three adaptation steps, a feedback pool A 2 TTA: Anchored-and-Agile Test-Time Adaptation for Evolving Traffic Sensor NetworksConference’17, July 2017, Washington, DC, USA DCRNN ASTGNN TGCN GWN Pretrain Retrain OL-N OL-AN TrafStm PECPM STKEC EAC STRAP ST-TTC STID STNorm iTrans DLinear STAEFormer Chronos2-FT-M† TimesFM-FT† Moirai2-FT† A2TTA(OL-AN) A2TTA(STAE) 0 5 10 15 20 25 30 35 40 MAE PEMS03 11.5 11.5 12.1 11.7 26.2 10.5 11.1 10.5 10.8 11.1 11.0 12.2 31.3↑ 10.8 11.0 13.5 10.9 11.7 9.4 13.3 14.2 13.9 9.8 8.9 DCRNN ASTGNN TGCN GWN Pretrain Retrain OL-N OL-AN TrafStm PECPM STKEC EAC STRAP ST-TTC STID STNorm iTrans DLinear STAEFormer Chronos2-FT-M† TimesFM-FT† Moirai2-FT† A2TTA(OL-AN) A2TTA(STAE) 0 10 20 30 40 PEMS04 19.3 18.7 21.0 20.2 141.8↑ 17.9 18.1 17.4 17.4 18.8 18.7 30.6 93.0↑ 17.9 20.1 21.4 17.9 19.5 16.0 18.9 20.9 20.7 15.4 14.0 DCRNN ASTGNN TGCN GWN Pretrain Retrain OL-N OL-AN TrafStm PECPM STKEC EAC STRAP ST-TTC STID STNorm iTrans DLinear STAEFormer Chronos2-FT-M† TimesFM-FT† Moirai2-FT† A2TTA(OL-AN) A2TTA(STAE) 0 5 10 15 20 25 30 35 PEMS05 10.3 10.4 10.3 11.1 23.2 10.0 13.8 9.8 10.1 10.1 10.2 14.7 29.9↑ 10.0 10.1 11.1 10.1 10.7 8.9 11.1 11.8 11.7 9.0 8.3 DCRNN ASTGNN TGCN GWN Pretrain Retrain OL-N OL-AN TrafStm PECPM STKEC EAC STRAP ST-TTC STID STNorm iTrans DLinear STAEFormer Chronos2-FT-M† TimesFM-FT† Moirai2-FT† A2TTA(OL-AN) A2TTA(STAE) 0 5 10 15 20 25 PEMS06 12.7 13.1 12.8 13.6 73.8↑ 12.3 17.2 11.9 12.2 12.9 12.6 17.8 48.6↑ 12.3 12.6 14.2 12.6 13.5 10.6 13.7 14.314.3 11.2 10.1 DCRNN ASTGNN TGCN GWN Pretrain Retrain OL-N OL-AN TrafStm PECPM STKEC EAC STRAP ST-TTC STID STNorm iTrans DLinear STAEFormer Chronos2-FT-M† TimesFM-FT† Moirai2-FT† A2TTA(OL-AN) A2TTA(STAE) 0 10 20 30 40 50 RMSE 19.4 19.5 23.2 19.6 34.1 17.7 18.8 17.7 18.1 18.5 18.4 20.3 48.4↑ 18.2 19.0 21.8 18.2 20.0 15.9 23.7 25.4 24.5 16.6 15.0 DCRNN ASTGNN TGCN GWN Pretrain Retrain OL-N OL-AN TrafStm PECPM STKEC EAC STRAP ST-TTC STID STNorm iTrans DLinear STAEFormer Chronos2-FT-M† TimesFM-FT† Moirai2-FT† A2TTA(OL-AN) A2TTA(STAE) 0 10 20 30 40 50 60 30.2 30.0 35.1 31.0 175.5↑ 28.4 28.4 27.7 27.8 29.1 29.2 44.1 120.0↑ 28.4 32.7 33.4 28.2 30.9 25.8 31.9 35.2 34.4 25.6 23.6 DCRNN ASTGNN TGCN GWN Pretrain Retrain OL-N OL-AN TrafStm PECPM STKEC EAC STRAP ST-TTC STID STNorm iTrans DLinear STAEFormer Chronos2-FT-M† TimesFM-FT† Moirai2-FT† A2TTA(OL-AN) A2TTA(STAE) 0 10 20 30 40 16.0 16.2 16.3 17.0 30.2 15.7 22.3 15.3 15.9 15.8 16.1 20.9 42.3↑ 15.7 15.8 16.6 15.7 16.8 13.9 18.6 19.9 19.3 14.3 13.1 DCRNN ASTGNN TGCN GWN Pretrain Retrain OL-N OL-AN TrafStm PECPM STKEC EAC STRAP ST-TTC STID STNorm iTrans DLinear STAEFormer Chronos2-FT-M† TimesFM-FT† Moirai2-FT† A2TTA(OL-AN) A2TTA(STAE) 0 5 10 15 20 25 30 35 40 19.5 20.3 20.2 20.8 91.2↑ 18.9 25.3 18.3 18.7 19.7 19.4 26.4 63.9↑ 18.9 19.6 21.1 19.3 21.2 16.1 23.1 24.2 23.8 17.1 15.3 DCRNN ASTGNN TGCN GWN Pretrain Retrain OL-N OL-AN TrafStm PECPM STKEC EAC STRAP ST-TTC STID STNorm iTrans DLinear STAEFormer Chronos2-FT-M† TimesFM-FT† Moirai2-FT† A2TTA(OL-AN) A2TTA(STAE) 0 10 20 30 40 50 60 70 80 MAPE (%) 34.2 29.4 32.8 31.8 56.6 29.7 30.0 28.8 30.2 32.4 31.3 35.1 72.8↑ 30.5 30.1 51.3 30.4 30.7 27.1 22.8 23.8 24.2 28.1 25.5 DCRNN ASTGNN TGCN GWN Pretrain Retrain OL-N OL-AN TrafStm PECPM STKEC EAC STRAP ST-TTC STID STNorm iTrans DLinear STAEFormer Chronos2-FT-M† TimesFM-FT† Moirai2-FT† A2TTA(OL-AN) A2TTA(STAE) 0 10 20 30 40 50 60 24.9 22.2 23.5 23.1 85.1↑ 22.1 21.9 19.9 21.3 26.9 24.6 41.5 67.4↑ 22.1 22.5 32.5 22.5 21.9 19.0 15.2 16.6 16.8 19.1 16.8 DCRNN ASTGNN TGCN GWN Pretrain Retrain OL-N OL-AN TrafStm PECPM STKEC EAC STRAP ST-TTC STID STNorm iTrans DLinear STAEFormer Chronos2-FT-M† TimesFM-FT† Moirai2-FT† A2TTA(OL-AN) A2TTA(STAE) 0 10 20 30 40 50 60 70 80 29.7 28.9 30.3 29.5 175.2↑ 28.1 31.5 26.2 28.1 28.9 29.2 72.7↑ 56.9 28.1 28.2 42.9 27.9 29.7 26.2 21.7 22.5 23.3 24.3 24.2 DCRNN ASTGNN TGCN GWN Pretrain Retrain OL-N OL-AN TrafStm PECPM STKEC EAC STRAP ST-TTC STID STNorm iTrans DLinear STAEFormer Chronos2-FT-M† TimesFM-FT† Moirai2-FT† A2TTA(OL-AN) A2TTA(STAE) 0 10 20 30 40 50 24.0 22.6 23.3 23.9 83.6↑ 22.3 26.0 21.4 21.9 25.7 24.3 35.7 62.9↑ 22.3 21.5 31.9 23.4 23.6 19.1 19.4 20.1 20.7 19.6 18.1 DCRNN ASTGNN TGCN GWN Pretrain Retrain OL-N OL-AN TrafStm PECPM STKEC EAC STRAP ST-TTC STID STNorm iTrans DLinear STAEFormer Chronos2-FT-M† TimesFM-FT† Moirai2-FT† A2TTA(OL-AN) A2TTA(STAE) 0 5 10 15 20 25 MAE PEMS08 15.7 15.2 16.3 15.8 55.1↑ 14.4 14.4 13.9 13.9 14.7 14.3 14.8 40.1↑ 14.4 15.1 18.1 14.6 15.5 12.5 14.2 14.9 15.0 12.9 11.7 DCRNN ASTGNN TGCN GWN Pretrain Retrain OL-N OL-AN TrafStm PECPM STKEC EAC STRAP ST-TTC STID STNorm iTrans DLinear STAEFormer Chronos2-FT-M† TimesFM-FT† Moirai2-FT† A2TTA(OL-AN) A2TTA(STAE) 0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 PEMS10 10.0 10.0 10.1 10.2 85.4↑ 9.6 9.6 9.4 9.6 9.7 9.6 11.6 25.3↑ 9.6 10.2 11.2 9.6 10.3 8.4 11.8 12.3 12.4 8.9 8.1 DCRNN ASTGNN TGCN GWN Pretrain Retrain OL-N OL-AN TrafStm PECPM STKEC EAC STRAP ST-TTC STID STNorm iTrans DLinear STAEFormer Chronos2-FT-M† TimesFM-FT† Moirai2-FT† A2TTA(OL-AN) A2TTA(STAE) 0 5 10 15 20 25 30 35 PEMS11 18.9 18.4 20.4 19.0 90.9↑ 17.4 19.9 16.9 17.3 20.5 17.9 24.7 58.8↑ 17.4 18.3 21.1 17.5 18.8 15.8 17.2 18.3 17.7 15.5 14.2 DCRNN ASTGNN TGCN GWN Pretrain Retrain OL-N OL-AN TrafStm PECPM STKEC EAC STRAP ST-TTC STID STNorm iTrans DLinear STAEFormer Chronos2-FT-M† TimesFM-FT† Moirai2-FT† A2TTA(OL-AN) A2TTA(STAE) 0 5 10 15 20 25 PEMS12 15.7 15.5 16.7 15.9 16.7 14.6 18.7 14.3 14.3 15.0 14.2 14.5 40.1↑ 14.6 15.2 17.9 14.9 15.6 12.5 14.7 15.7 15.3 12.5 11.3 DCRNN ASTGNN TGCN GWN Pretrain Retrain OL-N OL-AN TrafStm PECPM STKEC EAC STRAP ST-TTC STID STNorm iTrans DLinear STAEFormer Chronos2-FT-M† TimesFM-FT† Moirai2-FT† A2TTA(OL-AN) A2TTA(STAE) 0 10 20 30 40 50 60 70 80 RMSE 25.7 25.3 29.2 25.3 64.9 23.9 23.8 23.2 23.2 24.0 23.7 23.8 55.6 23.9 25.9 27.5 24.0 25.9 21.0 25.1 26.2 26.0 22.0 20.0 DCRNN ASTGNN TGCN GWN Pretrain Retrain OL-N OL-AN TrafStm PECPM STKEC EAC STRAP ST-TTC STID STNorm iTrans DLinear STAEFormer Chronos2-FT-M† TimesFM-FT† Moirai2-FT† A2TTA(OL-AN) A2TTA(STAE) 0 10 20 30 40 50 16.4 16.7 17.6 16.6 87.7↑ 15.8 15.9 15.5 15.8 16.0 15.9 17.5 37.6 15.8 16.6 17.7 15.8 17.1 13.8 20.6 21.1 21.3 14.8 13.3 DCRNN ASTGNN TGCN GWN Pretrain Retrain OL-N OL-AN TrafStm PECPM STKEC EAC STRAP ST-TTC STID STNorm iTrans DLinear STAEFormer Chronos2-FT-M† TimesFM-FT† Moirai2-FT† A2TTA(OL-AN) A2TTA(STAE) 0 10 20 30 40 50 30.7 30.6 36.7 31.0 117.8↑ 28.6 32.2 27.8 28.4 33.7 29.1 38.0 81.1↑ 28.6 29.5 33.4 28.7 31.3 25.7 32.4 34.4 32.8 26.2 23.9 DCRNN ASTGNN TGCN GWN Pretrain Retrain OL-N OL-AN TrafStm PECPM STKEC EAC STRAP ST-TTC STID STNorm iTrans DLinear STAEFormer Chronos2-FT-M† TimesFM-FT† Moirai2-FT† A2TTA(OL-AN) A2TTA(STAE) 0 20 40 60 80 27.1 27.2 30.9 27.3 27.2 25.4 32.7 24.8 25.1 25.8 25.0 24.9 60.3 25.4 26.4 29.6 25.7 27.7 22.7 27.7 29.7 28.6 22.9 21.1 DCRNN ASTGNN TGCN GWN Pretrain Retrain OL-N OL-AN TrafStm PECPM STKEC EAC STRAP ST-TTC STID STNorm iTrans DLinear STAEFormer Chronos2-FT-M† TimesFM-FT† Moirai2-FT† A2TTA(OL-AN) A2TTA(STAE) 0 10 20 30 40 50 60 MAPE (%) 23.8 20.3 21.7 21.6 57.9↑ 20.9 20.7 19.0 20.3 24.0 21.4 26.1 58.0↑ 20.9 21.0 40.1 22.1 20.9 17.1 17.5 18.3 18.6 17.1 16.0 DCRNN ASTGNN TGCN GWN Pretrain Retrain OL-N OL-AN TrafStm PECPM STKEC EAC STRAP ST-TTC STID STNorm iTrans DLinear STAEFormer Chronos2-FT-M† TimesFM-FT† Moirai2-FT† A2TTA(OL-AN) A2TTA(STAE) 0 20 40 60 80 100 35.6 32.8 34.1 34.1 988.5↑ 34.1 34.6 33.1 35.7 33.7 34.4 73.3 137.5↑ 34.1 37.3 46.8 33.4 34.2 30.8 27.8 28.6 29.2 30.4 28.7 DCRNN ASTGNN TGCN GWN Pretrain Retrain OL-N OL-AN TrafStm PECPM STKEC EAC STRAP ST-TTC STID STNorm iTrans DLinear STAEFormer Chronos2-FT-M† TimesFM-FT† Moirai2-FT† A2TTA(OL-AN) A2TTA(STAE) 0 10 20 30 40 50 60 27.5 23.6 26.5 24.7 79.1↑ 23.9 26.8 22.5 24.2 33.3 26.0 42.6 78.8↑ 23.9 27.7 41.6 24.7 23.9 22.7 21.9 23.1 23.2 21.3 19.8 DCRNN ASTGNN TGCN GWN Pretrain Retrain OL-N OL-AN TrafStm PECPM STKEC EAC STRAP ST-TTC STID STNorm iTrans DLinear STAEFormer Chronos2-FT-M† TimesFM-FT† Moirai2-FT† A2TTA(OL-AN) A2TTA(STAE) 0 10 20 30 40 50 60 70 28.4 25.1 28.2 26.0 27.0 25.0 27.4 23.2 24.5 28.2 24.5 27.2 90.1↑ 25.0 29.5 48.1 27.6 25.6 21.7 22.8 24.3 24.4 20.5 19.5 † TSFM-FT: all-sensor Avg reference (layout preview only); all other bars: new-sensor Avg. Static STGNNNaïveEvolving ContinualRetrieval / TTCOther StaticTSFM (FT)†Ours Figure 14: New-sensor Avg errors on the remaining eight datasets. of 512 windows, an update interval of 64 windows, three warm- up epochs, and three local steps. The learning-rate anchor is 10 −3 for A 2 TTA(STAE) on all three datasets and for A 2 TTA(OLAN) on PEMS05; it is 3×10 −3 for A 2 TTA(OLAN) on PEMS03 and PEMS06. Conference’17, July 2017, Washington, DC, USAYin et al. Q1 low Q2Q3Q4 high Drift-severity quartile 0.0 2.5 5.0 7.5 10.0 12.5 15.0 MAE reduction vs frozen (%) (a) Traffic-distribution drift Q1 low Q2Q3Q4 high Drift-severity quartile 0.0 2.5 5.0 7.5 10.0 12.5 15.0 (b) Graph-density change Q1 low Q2Q3Q4 high Drift-severity quartile 0.0 2.5 5.0 7.5 10.0 12.5 15.0 (c) Sensor churn −0.20.00.2 Spearman ρ (association only) A²TTA(OL-AN) · 5-seed A²TTA(STAE) · 5-seed A²TTA(OL-AN) · 1-seed A²TTA(STAE) · 1-seed Evidence tier p=.275 p=.255 p=.541 p=.644 −0.20.00.2 Spearman ρ (association only) p=.972 p=.034 p=.182 p=.093 −0.20.00.2 Spearman ρ (association only) p=.852 p=.052 p<.001 p<.001 A²TTA(OL-AN) · five-seed primary A²TTA(OL-AN) · single-seed breadth A²TTA(STAE) · five-seed primary A²TTA(STAE) · single-seed breadth Figure 15: Drift-severity diagnostics. A 2 TTA(OLAN) A 2 TTA(STAE) PEMS03 PEMS04 PEMS05 PEMS06 PEMS07 PEMS08 PEMS10 PEMS11 PEMS12 TFNSW 0.10.3 -0.30.2 0.40.3 -0.00.5 0.10.2 0.20.1 0.10.1 0.10.2 0.10.2 -1.2-0.5 Mean MAE gain over global-only TTA (%) A 2 TTA(OLAN) A 2 TTA(STAE) 6.96.6 7.79.2 5.04.6 6.15.8 6.76.6 5.05.2 4.03.7 7.39.2 5.75.8 26.819.1 Mean MAE gain over backbone (%) A 2 TTA(OLAN) A 2 TTA(STAE) PEMS03 PEMS04 PEMS05 PEMS06 PEMS07 PEMS08 PEMS10 PEMS11 PEMS12 TFNSW 52.080.0 25.079.2 90.581.0 57.181.0 56.052.0 72.060.0 75.055.0 33.348.1 70.866.7 19.033.3 Yearly win rate over global-only TTA (%) A 2 TTA(OLAN) A 2 TTA(STAE) 100.0100.0 100.0100.0 100.0100.0 100.0100.0 100.0100.0 100.0100.0 100.0100.0 96.3100.0 100.0100.0 100.0100.0 Yearly win rate over backbone (%) −1.5 −1.0 −0.5 0.0 0.5 1.0 1.5 5 10 15 20 25 0 20 40 60 80 100 0 20 40 60 80 100 Long-term breadth across ten datasets (one pre-specified seed) Figure 16: Long-term single-seed breadth check. Each dataset-backbone pair is normalized by its own paper config- uration before averaging, so an aggregate learning-rate point that is a default for only some pairs need not equal zero. Bands show variation across datasets. The learning-rate changes in Avg-MAE for A 2 TTA(OLAN) and A 2 TTA(STAE), respectively, are+0.51% and+0.39% at 10 −4 ,+0.11% and−0.12% at 3×10 −4 ,−0.05% and−1.30% at 3×10 −3 , and+2.75% and+1.59% at 10 −2 . With one adaptation step, the changes are +0.35% and−1.98%; with a pool of 128 windows, they are+1.83% and−1.25%. Across the other settings, the largest absolute mean change is 2.31%. Negative values denote lower Avg-MAE. The de- fault configuration therefore offers a reasonable accuracy-computation balance without requiring a separate exhaustive search for each stream. 1e-43e-41e-33e-30.01 4 2 0 2 4 Avg-MAE vs default (%) max || 2.8% TTA learning rate 1235 5 4 3 2 1 0 1 max || 2.0% TTA steps / batch 1282565121024 5 4 3 2 1 0 1 2 max || 2.3% delayed-label pool | | 3264128256 5 4 3 2 1 0 1 Avg-MAE vs default (%) max || 2.0% update interval K (windows) 135 2.0 1.5 1.0 0.5 0.0 0.5 1.0 max || 1.0% calibrator warm-up (epochs) 135 2 1 0 1 max || 1.1% local-clone steps A2TTA(OL-AN)A2TTA(STAE)paper default(s) Figure 17: One-at-a-time hyperparameter sensitivity. A.8 Ablation Study Details The ablation in Figure 6 starts from the same full stack for both backbones: a frozen forecaster, node-conditioned FiLM, global up- dates from matured labels, and a disposable context-weighted local clone. “w/o local clone” retains the global update but removes per- window specialization. “FiLM→affine” keeps adaptation and the clone but replaces input-conditioned modulation with a static scale and shift. “w/o online TTA” warm-starts FiLM and then freezes it during the test stream, while “backbone only” removes the calibra- tion stack. All variants process one window at a time, release labels after 12 windows, and trigger global adaptation every 64 windows. Avg-MAE is the mean of the cumulative scores for horizons 1 to 12. Values are means and standard deviations over seeds 51–55, with years averaged within each seed. Reverting to the frozen backbone increases absolute Avg-MAE by 0.58–1.12 for Online-AN and 0.52–1.87 for STAEFormer, or 6.5% and 6.7% on average relative to the full model. Replacing FiLM with affine costs 0.41–0.72 and 0.29–1.50, respectively, while removing the local clone costs 0.07–0.25 and 0.05–0.53. Freezing FiLM af- ter warm-up raises Avg-MAE by 0.03–0.11 for Online-AN and by 0.09–0.13 for STAEFormer on PEMS03 to PEMS05. STAEFormer on PEMS06 is the exception: the warm-up-only variant reaches 11.46±0.22, compared with 12.18±0.58 for full A 2 TTA, and is better in four of five seeds. The rerun therefore supports conditional FiLM and local refinement consistently, while online updating is helpful in most, but not all, settings. A.9 Case Study Details The case in Figure 9 uses only cohort membership and traffic vari- ance for selection, not relative forecast errors. We take the first sensor in the new/high-variance cohort by metadata order (sen- sor ID 601213; graph index 14) and its highest-volatility day, then average predictions from seeds 51 and 52. The rerun evaluates one window at a time and releases labels after 12 steps. Panels (a) and (b) cover all 288 five-minute windows of the selected day. At horizon 1, A 2 TTA reduces trace MAE from 21.51 to 20.00 with Online-AN and from 20.75 to 18.43 with STAEFormer. At horizon 12, the corresponding changes are 34.63 to 25.54 and 23.85 to 21.37. A 2 TTA: Anchored-and-Agile Test-Time Adaptation for Evolving Traffic Sensor NetworksConference’17, July 2017, Washington, DC, USA Panels (c) and (d) reportMAE backbone −MAE A 2 TTA for the 366 sen- sors with valid paired errors, comprising 207 existing and 159 new sensors; positive values indicate improvement. With Online-AN, 206 of 207 existing sensors and all 159 new sensors improve. With STAEFormer, the counts are 204 of 207 and 157 of 159. Mean per- sensor MAE falls by 7.29% relative to Online-AN and 2.62% relative to STAEFormer. The reductions remain similar across existing and new sensors: 7.24% versus 7.36% for Online-AN, and 2.41% versus 2.90% for STAEFormer. This case is illustrative; the multi-dataset, multi-seed experiments provide the aggregate evidence. A.10 Mechanism Visualization Figure 18 uses a separate legacy-batched seed-51 PEMS06-2015 A 2 TTA(STAE) diagnostic. It inspects learned representations and does not contribute to the accuracy tables. We record internal quan- tities only after delayed feedback is available. For every retained window-sensor pair, we extract the penultimate FiLM features from the persistent global calibrator and its context-specialized dispos- able clone. The two feature sets are concatenated before fitting one shared Uniform Manifold Approximation and Projection (UMAP). Separate fits would make their coordinate systems incomparable. For the heatmaps, each cell first averages over sensors and then over chronological windows whose forecast target begins in that clock hour. Joint UMAP 1 Joint UMAP 2 Joint UMAP 1 Joint UMAP 2 Existing sensor New sensor 515304560 Forecast horizon (min) 00:00 04:00 08:00 12:00 16:00 20:00 Hour of day 515304560 Forecast horizon (min) 00:00 04:00 08:00 12:00 16:00 20:00 0006121824 Hour of day 0 2 4 6 8 Mean absolute correction (flow) 0.0 0.5 1.0 1.5 2.0 2.5 Mean absolute refinement (flow) (a) Persistent global FiLM features (b) Context-specialized local features (c) Global correction | ̂ y g − ̂ y base |(d) Local refinement | ̂ y l − ̂ y g | Figure 18: Global and local calibration mechanisms on PEMS06-2015. The shared projection retains a clear time-of-day organization in both representations, while the local clone makes comparatively small paired movements within this structure. The correction maps give the same two-stage picture in output space: averaged over the captured stream, the global calibrator changes the frozen forecast by 4.40 flow units in absolute value, whereas the local clone adds a 0.90-unit refinement, or 20.4% of the global correction magnitude. Both corrections concentrate in the more active daytime regimes and vary across forecast horizons. Thus, the local clone acts as a targeted adjustment to a stable global adaptation rather than replac- ing it. This single-run visualization is mechanistic and illustrative. The ablations and multi-seed experiments provide the quantitative evidence.

Instant research discovery