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Toward Generalizable Graph Learning for 3D Engineering AI: Explainable Workflows for CAE Mode Shape Classification and CFD Field Prediction
Tong Duy Son, Kohta Sugiura, Marc Brughmans, Andrey Hense, Zhihao Liu, Amirthalakshmi Veeraraghavan, Ajinkya Bhave, Jay Masters, Paolo di Carlo, Theo Geluk
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Summary
This paper presents a physics-aware graph learning framework for 3D engineering AI, designed to handle heterogeneous data such as FE models and CFD meshes. By converting engineering assets into graph representations processed by Graph Neural Networks (GNNs), the framework supports CAE vibration mode shape classification and CFD aerodynamic field prediction. The approach emphasizes interpretability, reusability across vehicle variants, and effectiveness under label scarcity, providing a practical workflow for engineering decision support.
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Graph Neural Networks → enables → CAE vibration mode shape classification
confidence 95% · The framework is validated on two automotive applications: CAE vibration mode shape classification
Graph Neural Networks → enables → CFD aerodynamic field prediction
confidence 95% · The framework is validated on two automotive applications: ... CFD aerodynamic field prediction.
Physics-aware graph representations → represents → Heterogeneous engineering assets
confidence 90% · heterogeneous engineering assets are converted into physics-aware graph representations
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Abstract
Abstract:Automotive engineering development increasingly relies on heterogeneous 3D data, including finite element (FE) models, body-in-white (BiW) representations, CAD geometry, and CFD meshes. At the same time, engineering teams face growing pressure to shorten development cycles, improve performance and accelerate innovation. Although artificial intelligence (AI) is increasingly explored in this domain, many current methods remain task-specific, difficult to interpret, and hard to reuse across development stages. This paper presents a practical graph learning framework for 3D engineering AI, in which heterogeneous engineering assets are converted into physics-aware graph representations and processed by Graph Neural Networks (GNNs). The framework is designed to support both classification and prediction tasks. The framework is validated on two automotive applications: CAE vibration mode shape classification and CFD aerodynamic field prediction. For CAE vibration mode classification, a region-aware BiW graph supports explainable mode classification across vehicle and FE variants under label scarcity. For CFD aerodynamic field prediction, a physics-informed surrogate predicts pressure and wall shear stress (WSS) across aerodynamic body shape variants, while symmetry preserving down sampling retains accuracy with lower computational cost. The framework also outlines data generation guidance that can help engineers identify which additional simulations or labels are valuable to collect next. These results demonstrate a practical and reusable engineering AI workflow for more trustworthy CAE and CFD decision support.
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- Source: https://arxiv.org/abs/2604.07781v1
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Toward Generalizable Graph Learning for 3D Engineering AI Explainable Workflows for CAE Mode Shape Classification and CFD Field Prediction Tong Duy Son, Kohta Sugiura, Marc Brughmans, Andrey Hense, Zhihao Liu, Amirthalakshmi Veeraraghavan, Ajinkya Bhave, Jay Masters, Paolo di Carlo, Theo Geluk Automotive engineering development increasingly relies on heterogeneous 3D data, including finite element (FE) models, body-in-white (BiW) representations, CAD geometry, and CFD meshes. At the same time, engineering teams face growing pressure to shorten development cycles, improve performance and accelerate innovation. Although artificial intelligence (AI) is increasingly explored in this domain, many current methods remain task-specific, difficult to interpret, and hard to reuse across development stages. This paper presents a practical graph learning framework for 3D engineering AI, in which heterogeneous engineering assets are converted into physics-aware graph representations and processed by Graph Neural Networks (GNNs). The framework is designed to support both classification and prediction tasks. The framework is validated on two automotive applications: CAE vibration mode shape classification and CFD aerodynamic field prediction. For CAE vibration mode classification, a region-aware BiW graph supports explainable mode classification across vehicle and FE variants under label scarcity. For CFD aerodynamic field prediction, a physics-informed surrogate predicts pressure and wall shear stress (WSS) across aerodynamic body shape variants, while symmetry preserving downsampling retains accuracy with lower computational cost. The framework also outlines data generation guidance that can help engineers identify which additional simulations or labels are valuable to collect next. These results demonstrate a practical and reusable engineering AI workflow for more trustworthy CAE and CFD decision support. KEY WORDS: 3D Engineering AI, Graph Neural Networks, Explainable AI, CAE, CFD, Automotive Engineering 1. Introduction Automotive product development relies heavily on simulation-driven engineering, where Computer-Aided En- gineering (CAE) and Computational Fluid Dynamics (CFD) are used to evaluate structural, vibro-acoustic, and aero- dynamic performance before physical prototypes are final- ized [1]. In structural development, finite element (FE) mod- els are used to study body stiffness, modal behavior, and noise, vibration, and harshness (NVH) performance, while aerodynamic simulations are used to predict drag, pressure distribution, wall shear stress, and flow behavior around the vehicle [2–4]. These analyses are central to engineering de- cisions on lightweighting, body structural refinement, aero- dynamic efficiency, and overall product performance. Vehicle development generates multiple digital artifacts across design, simulation, testing, and validation workflows. These artifacts include 3D CAD geometry, body-in-white (BiW) and trimmed-body representations, finite element models, CFD surface meshes with field data, and test and validation measurements. In practice, these assets are dis- tributed across different tools, teams, sensor layouts, and configuration definitions. As a result, engineering knowl- edge is often fragmented across domains, making it difficult to reuse historical data and build AI workflows that operate consistently across the development process. AI adoption is accelerating in the automotive industry be- cause it offers a way to reduce repetitive expert effort and accelerate engineering decision-making. In CAE structural dynamics, AI can support structural interpretation, mode assessment, cross-variant comparison, and linkage with op- The authors are with Siemens Digital Industries Software, Leuven, Belgium. Contact Email: son.tong@siemens.com. This work is part of the ROBUSTIFAI project (grant agreement No. 101212818) funded by Horizon Europe – the Framework Programme for Research and Innovation. The work also benefited from the Flanders Innovation & Entrepreneurship VLAIO funded project SATISFY.AI. erational behavior during the development process [5,6]. In particular, vibration mode shape classification (e.g., bending, torsion, pumping, and local modes) remains time consum- ing and often depends on specialist judgment, which limits scalability when many model variants or iterations must be evaluated. In CFD, the motivation is complementary. High fidelity aerodynamic simulation is expensive, and field pre- diction is often needed for design exploration, optimization, and trade-off analysis [7–9]. Recent graph-based surrogates have shown that mesh-aware learning can accelerate fluid- related prediction while preserving more geometric structure than purely grid-based methods [10]. Both CAE and CFD therefore share a common opportu- nity: they require learning from complex 3D spatial struc- tures, yet they also require outputs that remain meaningful to engineers. Existing 3D AI methods address parts of this problem, but each comes with tradeoffs. Voxel and CNN approaches struggle with industrial geometric scale, point-based meth- ods often weaken explicit topology, and conventional surro- gates depend heavily on manual feature design [7, 11–13]. Physics-informed learning improves consistency with gov- erning principles, and graph-based methods preserve re- lational structure more naturally than grids or unordered points, but most published workflows are still tailored to one dataset or one narrowly defined task [14,15]. For engineering deployment, four challenges remain es- pecially important: 1. Data requirement: reliable models need to be built un- der limited data availability, without requiring large numbers of simulations or costly large-scale testing campaigns. 2. Interpretability and explainability: engineers need trustworthy models that not only predict or classify but arXiv:2604.07781v1 [eess.SY] 9 Apr 2026 Full VehicleTrim BodyFE Body-in-WhiteBody Design Transferable Across simulation variants and test data Generalizable Usable across historical data and workflows Explainable Results reflect engineering intuition Data Generation Guide additional simulations and labels Classification: Mode Shape Recognition (torsion, bending, pumping...) Prediction: external aerodynamic field (pressures, wall shear stress) Figure 1: Overview of the proposed graph learning framework for 3D engineering AI. Heterogeneous 3D models are mapped into engineering-guided graph representations that support CAE mode shape classification, CFD aerodynamic field prediction, and data generation workflow. also help connect data-driven inference with physical reasoning. 3. Reuse across variants: models should remain useful across related vehicle programs, mesh layouts, and con- figuration changes rather than only within one fixed dataset. 4. Industrial practicality: workflows must operate under heterogeneous data definitions, limited labels, and the need for engineering review rather than only benchmark accuracy. Despite rapid progress in industrial AI, current pipelines are still often node-specific, case-specific, or weakly con- nected to the engineering entities that engineers actually use in review. They also provide limited guidance on where new simulations, labels, or variant studies are most valuable once a surrogate or classifier is deployed. This gap is es- pecially important in automotive development, where CAE, CFD models and test data are closely related in practice but remain difficult to reuse consistently across variant programs and workflow stages. This paper addresses that gap by formulating a graph- based framework. The key idea is to transform 3D engineer- ing inputs into graph representations whose nodes, edges, and attributes retain physically meaningful structure while remaining flexible enough to support different downstream tasks. The proposed framework is physics-informed through engineering intuition embedded in graph construction, fea- ture definition, pooling design, and task formulation. It combines a shared engineering representation strategy with use case specific graph neural network (GNN) architectures. The framework is validated on two representative engineer- ing use cases: BiW mode shape classification and aerody- namic field prediction. Although the present demonstrations focus on FE-derived BiW and CFD surface data, the same formulation is intended to be extensible to other engineer- ing assets, such as CAD and trimmed-body representations, when they can be mapped into physically meaningful graph regions and relations. The main contributions of this work are as follows: 1. Graph-based engineering workflows for heterogeneous 3D assets, demonstrated on BiW data and CFD surface data, and extensible to CAD and trimmed body assets. 2. Region-aware BiW graphs and a hierarchical graph- attention explainable mode shape classification across BiW and FE, testing variants under severe label scarcity. 3. Physics-informed aerodynamic surrogates based on sur- face graphs for efficient pressure and WSS field predic- tion, enabled by symmetry-aware graph preprocessing. 4. An integrated workflow perspective in which explain- ability and uncertainty analysis support data generation in engineering practice. Explainability and uncertainty are considered in this work from a workflow perspective. In particular, data generation is framed as a means of prioritizing future simulations or labels, rather than as a fully validated closed-loop contribu- tion. Finally, although other AI architectures, particularly transformer-based models, may also support similar objec- tives, the present work focuses on GNNs because they are well suited to limited data settings and allow prior physical information to be incorporated through graph construction and message passing. The remainder of this paper is organized as follows. Sec- tion 2 reviews related works on CAE mode shape classi- fication, CFD surrogate modeling, and 3D graph learning. Section 3 presents the proposed AI framework. Sections 4 and 5 present the main results of CAE and CFD use cases, respectively. Section 6 discusses and concludes the paper. 2. Background This section reviews the technical background and prior work most relevant to 3D AI applications in CAE and CFD. It also considers the present study within broader discussions on reusable and domain-adapted AI frameworks in computa- tional science, where clarity of scope and rigor of evidence remain especially important [16]. 2.1 CAE 3D Mode Shape Recognition 3D mode shape recognition is a long standing desired capa- bility in automotive CAE because engineers must interpret finite element models, understand modal deformation pat- terns, and relate them to NVH performance, stiffness targets, and design trade-offs [1, 2, 6, 17]. In addition, there is an emerging need for mode shape recognition to extract modal KPIs from CAE modal analysis result files for NVH data- driven modelling. Traditional workflows rely on simulation outputs followed by manual expert classification of torsion, bending, pumping, and local structural modes, often requiring repeated review across vehicle variants and development cycles. Although valuable, this process is expensive when multiple body ar- chitectures, mesh densities, and subsystem changes must be compared under tight program schedules. Early attempts to automate mode interpretation relied on rule-based systems, modal parameter estimation, modal assurance criterion (MAC), and hand-crafted features ex- tracted from structural simulations [2, 18]. Classical super- vised learning methods and other feature-based classifiers improved automation but still depended heavily on expert- defined preprocessing and often remained tied to a particular vehicle or mesh representation. More recently, graph-based learning has emerged as a promising direction for struc- tural data because it can preserve regional connectivity and modal relationships more naturally than flat feature vectors or purely geometric point sets [15]. The recent automotive study showed that graph convolutional networks can sup- port structural mode classification directly from engineering representations, highlighting the practical potential of graph learning in this domain [5]. However, three limitations remain. First, most current approaches have limited cross-model transfer, especially be- tween different body platforms and between simulation and testing data. Second, explainability remains insufficient for engineering review, since high classification performance alone does not reveal why a mode is assigned to a partic- ular structural category. Third, existing approaches rarely provide a broader framework for exploiting historical en- gineering data across vehicle programs, even though such reuse is central to industrial value. 2.2 CFD External Aerodynamic Surrogate 3D aerodynamic prediction is another major target for auto- motive AI because CFD remains essential for drag reduction, flow control, thermal management, and energy-efficiency optimization [3,4]. In industrial practice, high fidelity CFD can require hours per simulation, making rapid design explo- ration or optimization expensive when various body variants, ride heights, or operating conditions must be evaluated. This has motivated a broad class of surrogate models that aim to approximate surface fields and integrated aerodynamic co- efficients while preserving sufficient fidelity for engineering use. Classical surrogate approaches include reduced order models and response surface methods, which can be effi- cient but often struggle when geometry, flow regime, or out- put dimensionality becomes highly nonlinear [13]. With the growth of deep learning, CNN based approaches have been used for flow field approximation, but they generally require regularized representations and are therefore less natural for high fidelity irregular vehicle surfaces [7, 11]. Mesh and graph based approaches, including MeshGraphNet models, have shown that message passing can better preserve local geometric structure and field interactions on irregular en- gineering domains [10]. Physics-informed learning further strengthens this direction by embedding consistency with governing principles directly into the learning process [14]. Recent automotive benchmark efforts have clarified this landscape. DrivAerNet++ established a large scale mul- timodal basis for aerodynamic learning on realistic car ge- ometries, while DrivAerStar presented a high fidelity aerody- namic prediction framework built on industrial scale meshing (12 million cells) and CFD solver outputs [8,9]. CarBench further highlights the importance of benchmark-driven eval- uation of neural surrogates for 3D car aerodynamics, in- cluding graph-based, transformer-based, and hybrid model families [19]. Despite this progress, three gaps remain especially rele- vant. First, CFD data generation remains expensive, creating a need for efficient strategies to determine where additional simulations will most improve a model. Second, many ap- proaches remain tightly coupled to a specific dataset, bench- mark, or configuration, which limits transfer to new geome- tries and engineering contexts. Third, interpretation remains difficult, particularly when engineers need to understand not only predicted values but also the surface regions and flow structures driving those predictions. 2.3 3D Engineering Data Representation and Learning The design of AI for engineering data depends strongly on representation. Voxel and grid based methods offer direct compatibility with standard CNN operations, but they of- ten sacrifice geometric efficiency and physical detail when complex 3D engineering objects are mapped onto regular domains [7,11]. Point based methods such as PointNet and PointNet++ avoid explicit meshing and capture local geomet- ric structure through hierarchical grouping, yet they do not provide a mechanism to incorporate engineer defined physi- cal relations such as FE element adjacency, component level coupling, or load path connectivity. [12]. Mesh and graph based methods are well suited to engineering assets because they preserve adjacency, connectivity, symmetry, and multi- scale interactions through explicit node-edge structure [20]. Transformer based learning is also increasingly relevant for 3D engineering tasks, particularly in settings where long range dependencies, global context, and multi-region in- teractions are important [19]. More broadly, recent works suggest that graph neural network, transformer, and hybrid architectures exhibit different accuracy-efficiency tradeoffs depending on mesh scale and prediction target. Across these representation families, the most important criteria for engineering use are structure preservation, phys- ical meaning, interpretability, scalability, transferability, and suitability for sparse or expensive labels. Accordingly, the present work focuses on graph-based learning not as an ex- clusive solution class, but as a practically motivated and structurally appropriate choice for the engineering settings considered in this research. 2.4 Explainable and Trustworthy AI in Engineering Black-box AI remains difficult to adopt in CAE and CFD practice because engineering decisions are not based on pre- diction accuracy alone. Engineers must understand which structural regions, geometric features, or flow patterns influ- ence a prediction before they can trust the model in design reviews or deploy it in iterative workflows. This has moti- vated the use of explainability tools such as attention visual- ization, saliency analysis, sensitivity analysis, and integrated gradients [15]. Although such techniques are useful, they often remain primarily data-driven and are not always con- nected back to domain knowledge, engineering terminology, or physically meaningful regional decomposition. Trustworthiness also requires uncertainty awareness. In engineering settings, uncertainty quantification is not only useful for measuring confidence; it also supports expert re- view and decisions about further data generation when pre- dictions are ambiguous or out of distribution. Bayesian ap- proximations and related uncertainty aware deep learning methods provide one path toward this goal [21]. Human-in- the-loop review is therefore not a fallback mechanism but a core part of responsible deployment, especially when model outputs are used to guide simulation budgets, structural inter- pretation, or aerodynamic design changes. For this reason, explainability, uncertainty awareness, and domain grounded interpretation must be treated as central properties of engi- neering AI rather than optional results. 3. AI Framework This section defines the common formulation used across the two use cases. Rather than treating CAE mode classification and CFD field prediction as completely unrelated AI prob- lems, the proposed approach formulates both as learning problems on physics-aware graphs derived from heteroge- neous 3D engineering data. In this paper, the foundation- style aspect lies in the reuse of a common graph abstraction and graph learning philosophy across engineering variants and task types, rather than in claiming one universal pre- trained model or one shared cross-domain network architec- ture. 3.1 Graph Formulation and Learning Pipeline Let an engineering sample be represented as a graph 퐺= (V, E, X, R), where V and E denote nodes and edges, X contains node attributes, and R contains edge or relation attributes. This formulation is intentionally generic so that it can represent FE models, BiW regional skeletons, CAD-derived surfaces, and CFD meshes under one abstraction. Depending on the use case, nodes may represent structural regions or surface samples, while edges encode physically meaningful relations such as adjacency, load-path coupling, local neighborhood, or symmetry. After graph construction, a use-case-specific graph neural network (GNN) encoder is used to learn latent node embed- dings through message passing. Each node is updated from its own attributes together with information aggregated from neighboring nodes and their relations, so the representation captures both local descriptors and higher-level interactions. At layer푙, a generic message passing update can be written as m (푙) 푖푗 = 휙 (푙) h (푙) 푖 , h (푙) 푗 , r 푖푗 , h (푙+1) 푖 = 휓 (푙) h (푙) 푖 ,□ 푗 ∈ N (푖) m (푙) 푖푗 , where휙 (푙) is the message function and휓 (푙) is the node update function, and□ denotes an aggregation operator such as sum, mean, or attention-weighted aggregation. After 퐿 layers, the encoder produces node embeddings that are passed to one or more task-specific output heads [20]. For graph-level classification, node embeddings are pooled into a graph representation z 퐺 = Pool h (퐿) 푖 푖∈ V , and decoded for class prediction. If the task benefits from explicit analytical descriptors, this pooled graph embedding can also be fused with engineered global features derived from the same graph construction, as in the region-aware structural descriptors used in Use Case A. For node-level regression, each node embedding is decoded directly, ˆ y 푖 = 푓 node (h (퐿) 푖 ), which is suitable for distributed outputs such as pressure or wall shear stress. More generally, the framework also supports coupled multi-head settings in which one graph sample produces several related outputs, such as hierarchical classification labels and location descriptors. Under this formulation, task variation is handled mainly through graph construction, supervision, architecture choice, engineered feature fusion, and output-head design. The commonality across use cases is therefore at the level of representation and engineering-AI principles, not at the level of a single cross-domain network architecture. Labelingthe Baseline Body-in-White Modes C123 based automated wireframe creation Page 1 FULL MODE SETTARGET MODE SET Automatic Wireframe GEOMETRY MODEL Nastran Output File 42 modes (0-100Hz) Target Modes Target Labels Import BIW FE model Automatic identification of structural skeleton Automatic creation of 1D beam elements Create RBE3 connections Conversion to PLOTEL and set creation Figure 2: Overview of data generation and mode shape labelling pipeline. 3.2 Engineering-Oriented Design Requirements From a practical engineering perspective, three requirements guide the framework. First, the graph must remain inter- pretable so that inputs and predictions can be traced back to recognizable regions, components, or surface areas already used in engineering review. Second, the same overall formu- lation should support different task types, including classifi- cation for structural interpretation and regression for aerody- namic field prediction, without requiring a completely dif- ferent representation philosophy for each application. Third, the workflow should remain useful under realistic industrial conditions, where data are heterogeneous, labels may be limited, and engineers need traceable predictions and expla- nation rather than only a numerical output. GNNs are well suited to this role because they preserve ir- regular engineering structure while allowing domain knowl- edge to be embedded through node definition, edge relations, and task-specific supervision. This engineering alignment is also what makes transfer learning more natural. When the graph is defined in terms of recognizable physical regions rather than raw mesh indices, the learned representation be- comes less dependent on a single simulation model and more reusable across related vehicle variants, mesh layouts, and engineering configurations. This is also important for engi- neering deployment. When explanation is mapped back to engineering regions or parameters, the model can indicate which structural zones or flow regions are driving the re- sult and therefore support human review more directly. The same workflow logic can be extended one step further. When region- or surface-level explanations are combined with un- certainty estimates, the model can help prioritize which new simulations, labels, or variant studies are most valuable to run next. In this paper, that uncertainty-guided data-generation role is introduced as a practical engineering workflow exten- sion rather than a fully validated end-to- end active-learning loop. In Use Case A, this supports hierarchical BiW mode classification on a canonical structural graph. In Use Case B, it supports surface-field prediction on downsampled aero- dynamic meshes. These two examples show how the same graph learning logic can be adapted to practical CAE and CFD workflows without changing the overall framework. 4. Use Case A: CAE Mode Shape Classification This use case addresses automatic classification of automo- tive body vibration mode shapes. Traditional approaches rely on handcrafted features or data-driven methods that treat structural components as generic nodes. Recent GNNs have shown promise by learning spatial relationships through mes- sage passing, but they do not inherently encode structural semantics. Without additional engineering structure, the network must infer distinctions such as floor, roof, pillar, or rail behavior purely from data, which becomes difficult un- der severe label scarcity and makes the resulting predictions harder to interpret in engineering review. The proposed region-aware architecture addresses these limitations by combining learned graph representations with analytical descriptors derived from 3D body-region group- ings. While standard global pooling aggregates node features uniformly, the present approach performs semantic-aware aggregation aligned with the hierarchical organization of the BiW. This design is motivated by how engineers interpret mode shapes in practice: they do not focus on individual nodes, but rather on the response of key structural regions and their couplings. For example, bending modes tend to concentrate response in rails and pillars, while pumping be- havior localizes more strongly in floor or roof structures. Compared with loss-driven physics-informed formulations, the engineering knowledge here is embedded directly into Restricted | © Siemens 2025 | Siemens Digital Industries Software Figure 3: Graph construction from wireframe. Figure 4: Canonical BiW regional decomposition used for region aware pooling and aggregation. the architecture through differentiable analytical operations rather than through additional physical constraint terms. The application focus spans both early-stage BiW devel- opment models and more detailed FE variants, where en- gineers repeatedly inspect modal analysis response to iden- tify torsional, bending, pumping, and local deformation pat- terns. Under this formulation, the main goal is not universal transfer, but robust reuse across related vehicle programs that share a canonical structural decomposition. The same region-based representation also creates a practical path to- ward testing workflows, in which measured responses can be aggregated onto the same skeletal topology. 4.1 Problem Formulation Each mode shape is treated as one graph sample. Start- ing from FE nodal displacement fields, the original model is aggregated onto a canonical BiW skeleton composed of expert defined body engineering regions. These regions cor- respond to consistent vehicle body structural regions such as front rails, pillars, roof zones, floor zones, side sills, and rear members. By mapping different FE models into the same regional decomposition, the learning problem is re- cast from vehicle specific classification into classification on a shared engineering graph. This is also what makes the architecture relevant across simplified BiW representations and more detailed FE layouts: the graph is tied to persistent structural regions rather than to a fixed node numbering or discretization. For this task, nodes represent BiW regions and edges encode four types of engineering relations: structural adja- cency, left-right symmetry, longitudinal load path coupling, and vertical roof-floor coupling. Each node carries aggre- gated regional features derived from the displacement field, including mean and RMS displacement magnitude, direc- tional response, signed vertical behavior, and related quanti- Figure 5: Confusion matrix for fine-grained Level-2 mode classification on the held-out multi-vehicle test set. Table 1: Held-out test performance under different training strategies. Training strategyL1 Acc. (%) L2 Acc. (%) Comb. (%) Reference-vehicle-only training90.881.685.3 Multi-vehicle training100.098.799.2 ties. Each edge carries compact relational features that reflect edge type, regional energy ratio, and phase agreement. The prediction target follows the hierarchy used in NVH engineering review. The model predicts a coarse Level-1 family, a fine-grained Level-2 subtype, and indicates poten- tial hybrid modes through confidence scores. This structure reflects how engineers assess mode shapes in practice: first by identifying the dominant global mechanism, then by refin- ing the interpretation into subtype and affected local regions. 4.2 Dataset Generation and Labelling The dataset comprises computed BiW modes from four ve- hicle programs, of which 326 were labeled by experienced NVH engineers and used for supervised training and evalua- tion. The vehicle set spans a mid-size sedan, compact sedan, luxury sedan, and sport sedan. Most labels come from the primary reference vehicle, while the additional vehicles con- tribute only 9, 2, and 5 labeled modes, respectively. This imbalance reflects the industrial scenario that motivated the work: historical programs are well understood, whereas new programs begin with only a small number of reviewed ex- amples. To increase the amount of training data, we created vari- ants of the original FE models with different vehicle charac- teristics, changing BiW beam stiffnesses, and materials. Fig- ure 2 illustrates the automatic data generation pipeline and wireframe creation from FE and BiW models using Siemens C123 technologies. Because all variants share a common Restricted | © Siemens 2026 | Siemens Digital Industries SoftwarePage 1 Feature Importance Figure 6: Illustrative explainability result for a mode shape classification, showing how model attribution can be mapped back to physically meaningful BiW regions. wireframe skeleton, MAC-based mode tracking between de- sign variations is straightforward and reliable, providing a consistent basis for hierarchical label assignment across the expanded dataset. This consistency does not extend to cross-vehicle or cross-geometry transfer. Expert labeling provides hierarchical supervision, and physics-aware aug- mentation expands the limited labeled dataset before graph attention network training. The relevant frequency band is approximately 0–100 Hz. The evaluation follows a stratified 70/15/15 train/validation/test split by vehicle and Level-2 class. 4.3 Graph Construction and Learning Results The graph topology is defined using engineering domain knowledge rather than raw FE connectivity alone. Fig. 3 shows the wireframe with the corresponding graph struc- ture, and Fig. 4 visualizes the canonical regional decompo- sition. The key idea is to preserve physically meaningful coupling while removing unnecessary dependence on the original mesh. The classifier uses a 4-layer graph attention encoder with 8 attention heads. To strengthen fine grained discrimination, the graph embedding is supplemented with a region-aware pooling module that computes analytical scalars from the regional responses, such as floor and roof energy fractions FE Model: BIW OEM1 (119 nodes) FE Model: BIW OEM2 (194 nodes) Test Data: BIW OEM3 (58 nodes) Test Data: BIW OEM4 (61 nodes) Figure 7: The four BiW structures with different body and node layout variants. and global vertical energy uniformity. These features are especially useful for separating physically similar but distinct classes, such as lateral bending versus floor pumping or roof pumping versus floor pumping. The network is trained with a multi-task objective that combines weighted cross-entropy for Level-1 prediction with focal loss for Level-2 prediction. The reported results are promising, especially considering the study scope: the training dataset comprises 226 labeled modes across four vehicles, with severe label imbalance and limited target-vehicle sample counts. A model trained only on the reference vehicle already achieves strong in-domain performance, reaching 100.0% at Level 2 on the held-out subset from that same vehicle. However, its performance degrades when applied to the other vehicle variants. When only 9, 2, and 5 labeled modes from the other three vehicles are added to the training dataset, the multi-vehicle training dataset model achieves 100% accuracy at Level 1, 98.7% at Level 2, and 99.2% on the combined metric on the held- out multi-vehicle test set. Only one of 76 test samples is misclassified, and that error remains within the same broader pumping family. Validation performance is 98.2%, and the hierarchical consistency rate is 100%, indicating that the joint heads preserve the intended label structure. In addition, the results show that the gains do not come from the GNN architecture alone. Multi-vehicle training with few target samples provides the significant improve- ment, followed by cross-vehicle feature alignment, data aug- mentation, and region-aware pooling. Compared with single vehicle training, the full multi vehicle setting improves Level- 2 accuracy by 17.1 percentage points, showing that transfer performance depends strongly on representation design and training protocol. 4.4 Explainability and Interpretation Engineering deployment requires more than a correct label. Vehicle dynamics and body engineers also need to under- stand which BiW regions drive a prediction and whether those regions correspond to recognizable structural behavior. Because the model operates on a small canonical regional graph, attribution can be mapped directly back to engineer- ing regions rather than to arbitrary FE node indices. Figure 6 illustrates this interpretation space. Torsion modes emphasize pillar-to-sill couplings and diagonal struc- tural paths, bending modes focus more strongly on vertically coupled rails and pillars, and pumping modes localize to floor or roof regions. This kind of explanation is valuable in engineering review because it helps analysts judge whether the model is using the same structural cues that would be considered in manual classification. 4.5 Generalizability and Transferability The most important outcome of this use case is the ability to achieve cross-vehicle transfer under severe label scarcity. Only four vehicles and a total of 26 labelled mode shapes were available in the beginning. To support reliable AI model training, one vehicle was selected for variant data generation using both a simulation-driven strategy guided by automo- tive engineering intuition and a complementary data-driven strategy. Because all vehicles are represented through the same region-aware graph, the model operates in a consistent engineering space even when the underlying FE models or test-derived representations differ substantially. This prop- erty is important in practice. A classifier trained on a single vehicle may perform well within its own domain, yet remain inapplicable to another vehicle because of different input nodes or generalize poorly because of differences in overall 3D body structure. By contrast, the proposed representation preserves regional semantics across vehicles and therefore supports transfer at the engineering level rather than only at the node or mesh level. Figure 7 shows the four BiW structures used in the study. In the reported experiments, the multi-vehicle aligned model correctly classifies all evaluated samples in the small test subsets of the other three vehicles at both coarse and fine- grained levels, whereas a single-vehicle baseline degrades on those same targets. This suggests that the canonical regional graph is doing more than reducing input size: it is capturing structural invariants that remain meaningful across vehicle programs. The engineering value lies not only in the reported classi- fication accuracy, but also in the reusable region-aware rep- resentation, which remains meaningful across discretization changes, layout differences, and related BiW variants. Im- portantly, the last two target cases are based on test data and contain substantially fewer sensor nodes than the FE-based cases, yet the model still produces strong results when these data are mapped to the same regional skeleton. These results provide encouraging evidence that the proposed represen- tation can support transfer between simulation and test do- mains, although a broader and more systematic simulation- to-test validation remains outside the scope of the present study. The findings also indicate that few-shot transfer is feasible across related BiW architectures and FE variants with different discretizations and layouts, despite the very limited number of target vehicle samples. From a practical standpoint, this suggests that a new vehicle program could be initialized with a small set of reviewed representative modes rather than a large vehicle-specific labeled dataset. These conclusions should nevertheless be interpreted in the context of the dataset size, and broader coverage across all relevant Figure 8: CFD data representation and preprocessing workflow, based on the DrivAerStar dataset generation [9]. structural regions would be desirable in future work. 5. Use Case B: CFD Aerodynamic Field Prediction This use case evaluates the framework on external aerody- namic field prediction from CFD-generated vehicle surface data. While use case A focuses on graph-level structural classification, this use case addresses dense node-level re- gression of aerodynamic surface fields. High fidelity aerody- namic simulation remains one of the main computational bot- tlenecks in vehicle concept development, particularly when many design variants must be screened within short devel- opment cycles. 5.1 Problem Formulation Each CFD sample is represented as a graph constructed from the vehicle surface mesh. The underlying data consist of high fidelity steady external aerodynamics simulations in which each sample includes surface geometry together with local pressure, wall shear stress (WSS), area, and surface normal information. Because the original meshes contain approximately 375k surface vertices, direct graph learning at full resolution is impractical for iterative training and model selection. The workflow therefore begins with symmetry- preserving downsampling to a graph of approximately 15k nodes while retaining the bilateral structure that is crucial for automotive exterior flow. For the downsampled surface graph, each node carries geometry-aware features such as normalized position, local area, surface normal, curvature, and distance to the vehicle centroid. Edges are defined through a local neighborhood graph with 푘= 16, enabling message passing on the irregular surface topology while preserving local geometric relations. Within this representation, the model predicts surface dis- tributed aerodynamic quantities, particularly pressure and WSS. 5.2 Dataset and Physics-Informed Learning The aerodynamic use case is based on a dataset of approxi- mately 10,000 CFD simulations generated in STAR-CCM+ for three DrivAer-style body configurations: Estateback, Restricted | © Siemens 2026 | Siemens Digital Industries SoftwarePage 1 Figure 9: Training and validation performance of the physics-informed aerodynamic surrogate, showing training process and prediction accuracy for pressure and wall shear stress. Figure 10: Quantitative performance comparison for aerodynamic field prediction: 푅 2 = 0.989 for pressure and 푅 2 = 0.985 for WSS, outperforming the evaluated baseline models. Fastback, and Notchback [8, 9]. The data are divided into 70% training, 15% validation, and 15% test sets, stratified by configuration, resulting in a held-out test set of about 1500 samples. Compared with the CAE use case, this provides a much larger and more uniform basis for assessing regression performance. The predictive backbone is an attention-based AeroGraph- Net with separate encoders for node and edge features, 6 message passing layers, 4 attention heads, and a decoder that outputs one pressure value and a 3-component WSS vector per node. The model size is approximately 2.3M parameters. Training is designed to stabilize field predic- tion through a combination of data-driven supervision and physics-informed regularization. The loss design is one of the technical features. Rather than relying solely on point- wise data fitting, the training objective combines data fidelity with physically motivated regularizers, including Bernoulli- style consistency, a mass conservation term, and WSS tan- gency to the surface. For the purposes of this paper, the key point is that these physics-informed terms systematically improve predictive quality relative to the corresponding data- only surrogate, albeit at the cost of increased training time. 5.3 Training and Prediction Performance The results indicate strong field prediction performance. The coefficient of determination 푅 2 quantifies the proportion of variance in the reference data explained by the model, with values closer to 1 indicating stronger predictive accuracy. Restricted | © Siemens 2025 | Siemens Digital Industries SoftwarePage 1 Validation: Pressure field Prediction Prediction Ground Truth Error Ground Truth Validation: Wall Shear Stress (WSS) Prediction Ground Truth Error Error Error Figure 11: External aerodynamic field prediction results, comparing predicted surface fields with CFD reference data. The full physics-informed model achieves 푅 2 = 0.989 for pressure and푅 2 = 0.985 for wall shear stress (WSS), together with a pressure mean absolute error (MAE) of 21.58 Pa and a WSS MAE of 0.49 Pa. These results compare favorably with the evaluated GNN-based baselines, including MLP, GCN, MeshGraphNet, and a data-only version of the pro- posed architecture. Relative to the data-only variant, the physics-informed formulation improves 푅 2 by 6.6 points for pressure and 10.6 points for WSS. The ablation studies show that symmetric downsampling is a central technical enabler of the workflow rather than a simple preprocessing convenience. Under the same 15k- node budget, the symmetry-preserving graph retains 99.8% bilateral correspondence. By comparison, random sampling reduces performance to 0.871 and 0.823, while curvature- based sampling reaches 0.912 and 0.891 for pressure and WSS, respectively. Relative to the full 375k-vertex sur- face, the symmetric 15k-node graph preserves near compara- ble predictive accuracy while substantially reducing training cost. From an engineering perspective, computational speed is equally important. Inference is reported at approximately 57 ms per sample on a GPU, representing a substantial speedup over the evaluated baselines. This makes the model valuable not only as a high-accuracy surrogate, but also as a practical source of field-level feedback during rapid design iteration. Additional studies indicate that edge-aware message pass- ing is important, that 푘= 16 provides the best trade- off between accuracy and computational cost, and that six message-passing layers outperform shallower alternatives. Across the Estateback, Fastback, and Notchback subsets, pressure 푅 2 remains consistently high, suggesting that the model generalizes across related body configurations rather than specializing to a single geometry type. The qualitative field visualizations are consistent with these quantitative results. Front stagnation regions, rear pressure-recovery zones, and high-shear regions are repro- duced with good fidelity, supporting the use of the model as a credible engineering surrogate for aerodynamic field prediction. Restricted | © Siemens 2026 | Siemens Digital Industries SoftwarePage 1 Figure 12: Explainability example highlighting regions that contribute to aerodynamic surface field prediction. 5.4 Explainability and Workflow Development The aerodynamic model also provides an interpretable pre- diction space. Attention based analysis and attribution maps indicate that the learned model focuses on physically mean- ingful regions such as front stagnation areas, rear end sep- aration zones, and underbody flow sensitive regions. This matters because explainability in engineering AI is only use- ful when it can be translated back into recognizable flow structures and body zones that engineers already use in de- sign review. This interpretability also makes the surrogate more action- able for geometry refinement and design trade-off studies, as dominant pressure and WSS regions can be linked back to recognizable body zones. The same information can also support uncertainty guided data generation. If predictive uncertainty or model disagree- ment rises in specific flow regions or for particular body shape variants, those signals can help engineers decide which additional CFD cases should be run to expand the training set most effectively. This is especially relevant for extend- ing coverage beyond the currently validated training domain, where new geometries or operating conditions may expose gaps in the surrogate. 5.5 Generalizability This use case shows that the graph learning philosophy used for BiW mode classification can also support high- dimensional aerodynamic field prediction. The shared ele- ment is not a single cross-domain pretrained model, but a common engineering strategy: convert irregular 3D assets into interpretable graphs, embed domain knowledge through graph construction and supervision, and adapt the output head to the task. Within the aerodynamic domain, this strategy can be reused across different 3D body shape vari- ants through a consistent surface graph representation and a symmetry-aware preprocessing pipeline. The aerodynamic study nevertheless has a clear scope. It is restricted to steady state external aerodynamics on the DrivAer dataset family, uses a surface based surrogate rather than a full 3D flow volume model, and shows reduced accu- racy under more extreme out-of-distribution conditions such as large yaw angles or substantial spoiler variations. These limitations do not diminish the present use case; instead, they define its valid operating range and highlight trustwor- thy, where explainability and uncertainty aware analysis are Restricted | © Siemens 2025 | Siemens Digital Industries SoftwarePage 1 Figure 13: Uncertainty-guided data generation concept. The current framework can indicate where additional CFD samples or simulations are likely to be most valuable. most valuable. Within a well characterized domain, the AI engineering can provide not only efficient aerodynamic field prediction, but also interpretable insight into the flow regions that govern the prediction and practical guidance for tar- geted data generation when additional CFD simulations are required. Future work may build on this foundation through uncertainty guided sampling and extension to latent-based representation sampling, as well as broader geometric and boundary condition variations. 6. Discussion and Conclusion This paper presented a reusable graph learning framework for 3D engineering AI, in which heterogeneous engineering data are represented as physics-aware graphs and processed through engineering-aligned workflows. Across the two au- tomotive use cases, the unifying principle is not a single cross-domain model, but the combination of engineering- informed graph representations, task specific prediction, and explanations grounded in meaningful physical entities. The contribution is therefore best understood not as a universal foundation model, but as a practical and reusable engineering AI paradigm for related tasks and simulation variants. The results demonstrate that graph-based learning can support different engineering tasks while preserving domain relevance and interpretability. In the CAE setting, a canon- ical regional graph enables mode classification across BiW and FE variants. In the CFD setting, a physics-informed surface graph enables pressure and wall shear stress predic- tion across body shape variants. Taken together, these use cases indicate that graph abstraction can provide a coherent basis for both reuse and interpretation. From an engineer- ing perspective, the framework offers the potential to reduce repeated expert effort in structural assessment and repeated field evaluation in aerodynamic design studies, while en- abling earlier feedback and more effective use of historical engineering data. 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