Paper deep dive
LettuceVisSim: A Simulator That Generates Lettuce Image Time-series for Vision-Based Reinforcement Learning
Ziye Zhu, Bert van 't Ooster, Congcong Sun, Eldert van Henten, Sjoerd Boersma
Intelligence
Status: succeeded | Model: Gemma-4-26B-A4B | Prompt: intel-v1 | Confidence: 93%
Last extracted: 9/16/2026, 8:55:50 AM
Summary
The paper introduces LettuceVisSim, a simulator designed to generate labelled time-series of lettuce crop images for vision-based reinforcement learning in controlled environment agriculture. The system integrates a process-based model (PBM) for shoot dry weight dynamics, a canopy layout algorithm to map biomass to visual representations, and a Unity rendering engine for efficient image generation. Validation results show high accuracy in reproducing shoot dry weight (R²=0.84) and projected area (R²=0.94), with the simulator successfully enabling the learning of lighting-control policies from synthetic data.
Entities (8)
Relation Signals (6)
LettuceVisSim → contains → Process-Based Model
confidence 95% · The simulator contains a process-based model (PBM) for shoot dry weight dynamics
LettuceVisSim → contains → Unity Rendering Engine
confidence 95% · a Unity rendering engine for image generation
Unity Rendering Engine → generates → RGB and segmentation images
confidence 95% · The Unity rendering engine converted canopy layout representations into RGB and segmentation images
Process-Based Model → simulates → Shoot Dry Weight
confidence 95% · The PBM reproduced shoot dry weight under dynamic plant-density management
LettuceVisSim → enables → Vision-Based Reinforcement Learning
confidence 90% · providing a proof of concept of vision-based reinforcement learning in CEA using LettuceVisSim
Process-Based Model → isbasedon → Van Henten lettuce model
confidence 90% · The PBM used in this study... well-established Van Henten lettuce model
Cypher Suggestions (0)
No Cypher suggestions yet.
Abstract
Abstract:Vision-based reinforcement learning holds strong potential for decision-making in controlled environment agriculture (CEA). However, its development is hindered by the scarcity of labelled crop images. To address this gap, LettuceVisSim, a lettuce growth simulator that generates labelled time series of crop images, was developed and validated. The simulator contains a process-based model (PBM) for shoot dry weight dynamics, a canopy layout algorithm for deriving canopy layout representations from shoot dry weight, and a Unity rendering engine for image generation. Five findings support the simulator. First, the PBM reproduced shoot dry weight under dynamic plant-density management with $\mathrm{R}^{2}=0.84$. Second, a piecewise cubic regression mapped shoot dry weight to potential projected area with $\mathrm{R}^{2}=0.94$. Third, the canopy layout representation was validated using 12 experimental datasets each having different dynamic environmental and spacing conditions. It reproduced the ground coverage ratio dynamics observed in measured images, achieving $\mathrm{R}^{2}=0.84$ when driven by measured shoot dry weight and $\mathrm{R}^{2}=0.40$ (0.76 excluding one outlier) when driven by PBM-simulated values. Fourth, the Unity rendering engine converted canopy layout representations into RGB and segmentation images at less than 10~ms. Fifth, a demonstration showed that a lighting-control policy can be learned and applied by observing only crop images that were generated with LettuceVisSim, providing a proof of concept of vision-based reinforcement learning in CEA using LettuceVisSim.
Tags
Links
- Source: https://arxiv.org/abs/2609.12505v1
- Canonical: https://arxiv.org/abs/2609.12505v1
Trouble viewing inline? Open PDF directly →
Full Text
110,758 characters extracted from source content.
Expand or collapse full text
LettuceVisSim: A Simulator That Generates Lettuce Image Time-series for Vision-Based Reinforcement Learning Journal: Biosystems Engineering Ziye Zhu Note: Agricultural Biosystems Engineering Group, Wageningen University & Research, The Netherlands Corresponding author: Corresponding email: ziye.zhu@wur.nl Bert van ’t Ooster Note: Agricultural Biosystems Engineering Group, Wageningen University & Research, The Netherlands Congcong Sun Note: Agricultural Biosystems Engineering Group, Wageningen University & Research, The Netherlands Eldert van Henten Note: Agricultural Biosystems Engineering Group, Wageningen University & Research, The Netherlands Sjoerd Boersma Note: Biometris, Wageningen University & Research, The Netherlands Abstract Vision-based reinforcement learning holds strong potential for decision-making in controlled environment agriculture (CEA). However, its development is hindered by the scarcity of labelled crop images. To address this gap, LettuceVisSim, a lettuce growth simulator that generates labelled time series of crop images, was developed and validated. The simulator contains a process-based model (PBM) for shoot dry weight dynamics, a canopy layout algorithm for deriving canopy layout representations from shoot dry weight, and a Unity rendering engine for image generation. Five findings support the simulator. First, the PBM reproduced shoot dry weight under dynamic plant-density management with R2=0.84R^2=0.84. Second, a piecewise cubic regression mapped shoot dry weight to potential projected area with R2=0.94R^2=0.94. Third, the canopy layout representation was validated using 12 experimental datasets each having different dynamic environmental and spacing conditions. It reproduced the ground coverage ratio dynamics observed in measured images, achieving R2=0.84R^2=0.84 when driven by measured shoot dry weight and R2=0.40R^2=0.40 (0.76 excluding one outlier) when driven by PBM-simulated values. Fourth, the Unity rendering engine converted canopy layout representations into RGB and segmentation images at less than 10 ms. Fifth, a demonstration showed that a lighting-control policy can be learned and applied by observing only crop images that were generated with LettuceVisSim, providing a proof of concept of vision-based reinforcement learning in CEA using LettuceVisSim. Keywords: Controlled Environment Agriculture , Vision-Based Reinforcement Learning , Synthetic Data Generation , Machine Vision , Crop Growth Model 1 Introduction Controlled environment agriculture (CEA) refers to food production systems in which crop growth takes place under artificially regulated indoor environmental conditions, it includes the greenhouse and plant factory production systems [Kozai et al., 2019, Chen et al., 2025]. By decoupling crop production from external weather variability, CEA offers a promising approach to address the growing global demand for food under increasing constraints on land and water availability, as well as rising climate change risks [Hossain et al., 2020, Guo and Shen, 2016]. To fully realise this potential, a key challenge lies in optimising crop growth, which requires the appropriate setting of climate control setpoints governing the growth environment [Van Henten, 1994a, Bakker et al., 1995]. Many control methods have been studied for this task. Optimal control has been used for lettuce in both greenhouses [Van Henten, 1994a, Xu et al., 2018] and plant factories [Xu et al., 2021] and model predictive control to greenhouse tomato production [Hu and You, 2022, Xu et al., 2025]. More recently, reinforcement learning (RL), a data-driven, learning-based control method [Sutton and Barto, 2018], has emerged as a promising new option, with reports for greenhouse tomato [An et al., 2021, Van Laatum et al., 2025] and lettuce [Morcego et al., 2023, Mallick et al., 2025] production. In these control studies, the crop state is usually the canopy biomass (dry weight, kg⋅m−2kg· m^-2), and assumed to be measured. In practice, however, dry weight is not frequently measured by destructive sampling. Such measurements are not accurate, and they make crop data scarce. This creates a clear gap between what these controllers assume and what is achievable in CEA, which limits the knowledge of their true potential [Gautron et al., 2022]. Vision-based RL [Mnih et al., 2015] holds potential to mitigate this gap, as it learns control directly from crop images rather than from biomass measurements. It is promising for two reasons. First, crop image acquisition is non-destructive and second, a time series of a biomass proxy can be estimated from them [Gupta and Ibaraki, 2014, Bumgarner et al., 2012, Concepcion Ii et al., 2020, Du et al., 2021]. Its main limitation, however, is data scarcity. Vision-based RL needs large amounts of labelled training data. One simple grasping task alone requires about 580,000 trajectories [Kalashnikov et al., 2018]. The datasets at such scale are generally not available in agriculture [Parr et al., 2021]. A common approach to mitigate this scarcity is generating data with simulators. Such simulators have been widely adopted in robotics [Zhao et al., 2020], drones [Song et al., 2021] and process control systems [Li et al., 2024]. To support development of vision-based RL in CEA, a simulator should generate time-series of crop images that are labelled with corresponding quantitative crop traits such as shoot dry weight, representing the crop state transition under dynamic environmental and management conditions and do so efficiently. However, no existing model meets this need. Existing approaches fall into two types. Process-based models (PBM) simulate biomass from physiological mechanisms [Di Paola et al., 2016]. These models cannot generate images. Another type of existing models are the Functional–structural plant models (FSPM) can render plant morphology [Buck-Sorlin, 2013], but these models are often static or computationally expensive [Louarn and Song, 2020]. Beyond crop growth models, generation models such as diffusion model can generate highly realistic images [Croitoru et al., 2023, Tan et al., 2025, Zangana et al., 2025], but they are slow at inference and provide no explicit link between pixels and traits such as shoot dry weight. Hence, no current method can generate labelled time-series crop images at the throughput that vision-based RL requires. In this study, we follow the hierarchical design proven in drone simulation [Song et al., 2021], where a PBM computes the system state. This state is then mapped to a visual representation, after which a game engine renders it into images. This design was applied to lettuce growth and present LettuceVisSim, an integrated lettuce simulator that generates time-series top-view canopy images labelled with shoot dry weight, as a function of temperature, light, CO2, and plant spacing. LettuceVisSim consists of three main modules: 1. A lettuce PBM simulating shoot dry weight in response to dynamic environmental conditions and spacing management. 2. A canopy layout algorithm that converts shoot dry weight into a canopy layout representation. 3. A Unity rendering engine that generates images from canopy layout representation. For the PBM, the well-established Van Henten lettuce model [Van Henten, 1994b] was adopted. It takes, among other, plant density as an input, but was developed and validated under a fixed density. CEA, however, routinely reduces density as the canopy expands, so its validity under dynamic spacing needs to be examined. The canopy layout algorithm consists of two steps. First, an empirical model maps shoot dry weight to the potential projected area (PPA), the top-view area of an isolated plant. Second, a uniform-grid construction combines PPA and plant density into a canopy layout that approximates the top-view canopy. From this layout, the ground coverage ratio (GCR) could be computed in the same way as for measured images. The Unity rendering engine then turns the canopy layout into top-view RGB and segmentation images, where the efficiency of image generation is the primary concern. This study validated LettuceVisSim as a data generator for vision-based RL through five research questions: 1. Does the PBM, originally developed under a fixed plant density, remain valid for predicting shoot dry weight dynamics under dynamic plant-density management? 2. How can shoot dry weight be accurately mapped to PPA across growth stages? 3. Can the proposed canopy layout representation reproduce GCR dynamics consistent with those derived from measured images under dynamic environmental and spacing conditions? 4. How efficiently can a Unity rendering engine generate images in terms of visual fidelity and computational performance? 5. Can images generated by the validated simulator, in principle, support vision-based RL training? 2 Material and methods 2.1 Simulator overview LettuceVisSim is a modular lettuce growth simulator consisting of three modules, as shown in Fig. 1: a PBM (Section 2.1.1) that simulates biomass accumulation in response to environmental variables and spacing management, a canopy layout algorithm (Section 2.1.2) that converts shoot dry weight per plant into a canopy layout representation, and a Unity rendering engine (Section 2.1.3) that generates synthetic images based on the canopy layout representation. Figure 1: Schematic diagram of LettuceVisSim. Rectangular boxes represent the three modules of the simulator: the Process-Based Model (PBM), the canopy layout algorithm, and the Unity rendering engine. Rounded boxes represent the output of each module: simulated shoot dry weight w w, canopy layout representation C, and synthetic RGB and segmentation images, respectively. At each image sampling time, the canopy layout algorithm and the Unity rendering engine are called sequentially to map the current shoot dry weight to synthetic images. In this simulator, shoot dry weight accumulation is simulated by the PBM at a temporal resolution Δtgrowth=5 t_growth=5 min. The image sampling interval is independently configurable, provided it is no shorter than Δtgrowth t_growth. At each image sampling time, the canopy layout algorithm converts the simulated shoot dry weight and plant density into a canopy layout representation, which is then passed together with the elapsed cultivation day tdayt_day, defined as the integer number of days since transplanting, to the Unity rendering engine to generate top-view RGB images and corresponding segmentation masks. The PBM used in this study has been validated and widely applied in many control studies [Boersma et al., 2022, Svensen et al., 2024, Xu et al., 2020] and is therefore only briefly described in the following section. The canopy layout algorithm and the Unity rendering engine are newly proposed in this study and are described in detail in the following sections. 2.1.1 Process based model This section presents a brief overview of the PBM used in this study; a detailed description is provided in Van Henten [Van Henten, 1994b]. In the original PBM, lettuce growth is formulated in continuous time as an ordinary differential equation (ODE). In this study, a discrete-time representation was obtained by numerically integrating the ODE with a fixed time step Δtgrowth t_growth. Let w w denote simulated shoot dry weight (g per plant). The PBM can be written as: dw^tdt=g(w^t,Tt,It,CO2,t,pdt,p), d w_tdt=g\! ( w_t,\,T_t,\,I_t,\,CO_2,t,\,pd_t,p ), (1) where T, I, CO2CO_2, pdpd denote air temperature (∘C), incident radiation (μmol⋅m−2⋅s−1 ·m^-2·s^-1), carbon dioxide concentration concentration (ppm) and plant density (plants ⋅m−2·m^-2), respectively, and p denotes model parameters. The state update used in the simulator was obtained with forward Euler integration: w^t+1=w^t+Δtgrowthg(w^t,Tt,It,CO2,t,pdt,p)⏟f(w^t,Tt,It,CO2,t,pdt,p), w_t+1= w_t+ t_growth\;g\! ( w_t,\,T_t,\,I_t,\,CO_2,t,\,pd_t,\,p )_f\! ( w_t,\,T_t,\,I_t,\,CO_2,t,\,pd_t,\,p ), (2) where w^t≈w^(t0+tΔtgrowth) w_t≈ w(t_0+t\, t_growth) and the inputs were assumed constant over each interval of length Δtgrowth t_growth. The detailed PBM equations and parameter definitions are provided in A. 2.1.2 Canopy layout algorithm The canopy layout algorithm converts the shoot dry weight input w∗w and plant density pdtpd_t into a canopy layout representation at each image sampling time step, where w∗=w =w when measured shoot dry weight is used and w∗=w^w = w when simulated shoot dry weight is used. This canopy layout representation describes a 1m21~m^2 top view of the canopy in a simplified form, as a set of circles in which each circle approximates the top-view projection of an individual plant. Each circle is parameterised by its centre coordinates and its radius. The canopy layout algorithm comprises a shoot dry weight–PPA mapping step and a uniform-grid construction step, as described next. The shoot dry weight–PPA mapping step defines an empirical regression model, denoted as fPPA:w∗↦PPAf_PPA:w , to convert shoot dry weight per plant w∗w into the corresponding PPA. Empirical regression models have been widely used to predict biomass from image-based traits such as PPA [Li et al., 2022, Baek et al., 2025]. Common formulations include linear, polynomial, logistic, and hyperbolic regression models, which can be used in an inverse manner to map shoot dry weight to PPA. Because such formulations apply a single function over the entire growth period, growth-stage-dependent changes in the relation between PPA and shoot dry weight may not be captured adequately. Therefore, in addition to these so called one-phase formulations, a two-phase formulation was considered, in which the growth period is divided into two growth phases separated by a transition point. Both one-phase and two-phase empirical regression models were treated as candidate implementations of fPPAf_PPA. Their mathematical formulations, parameter estimation, and comparative evaluation for model selection are described later in Experiment 2. The uniform-grid construction step uses fPPAf_PPA to convert shoot dry weight w∗w and plant density pdtpd_t into a canopy layout representation C, which approximates the top-view lettuce canopy within the camera field of view (FoV). This representation corresponds to the top-view canopy captured by a fixed overhead camera mounted above the centre of the cultivation area, with a monitored area of 1m21~m^2. This construction relies on three simplifying assumptions: (1) plants are distributed uniformly within the cultivation area; (2) boundary effects are taken into account by including partially visible plants along the edges of the image; and (3) canopy closure is modelled as geometric overlap of PPA, neglecting physical deformation or architectural adaptation caused by mechanical contact between neighboring plants. Besides w∗w and pdtpd_t, the FoV dimensions (L×W)(L× W) are also taken as input. The uniform-grid construction step proceeds in four stages: grid initialisation, grid expansion for boundary handling, radius computation and FoV-intersection filtering, and canopy layout construction. In grid initialisation stage, the FoV aspect ratio α=L/Wα=L/W and plant density pdtpd_t are used to determine the grid dimensions, from which a regular set of plant centres PoptP_opt is generated within the FoV. In grid expansion for boundary handling stage, this grid is expanded by integer shifts along both spatial directions, yielding an extended candidate set PextP_ext. In radius computation and FoV-intersection filtering stage, the projection radius is computed as r=fPPA(w∗)/πr= f_PPA(w )/π, and only those centres whose circular projections intersect the FoV are retained, resulting in PfinalP_final. In the canopy layout construction stage, the canopy layout representation C is constructed as the set of circles centred at PfinalP_final with common radius r. Together, these four stages define the canopy layout algorithm, which is summarised in Algorithm 1. Algorithm 1 Canopy layout algorithm Input: w∗w : shoot dry weight per plant; pdtpd_t: plant density; L×WL× W: size of field of view (FoV), corresponding to a top-view area of 1 m2m^2 Output: Canopy layout representation C as a set of circular canopy projections in two-dimensional space // 1. Grid initialisation α←L/Wα← L/W ; col←⌈pdt⋅α⌉col← pd_t·α ; row←⌈pdtcol⌉row← pd_tcol dx←Lcol+1,dy←Wrow+1dx← Lcol+1, 8.50012ptdy← Wrow+1 Popt←(i⋅dx,j⋅dy)|i=1,…,col;j=1,…,rowP_opt←\(i· dx,\ j· dy)\ |\ i=1,…,col;\ j=1,…,row\ // 2. Grid expansion for boundary handling xmin,xmax←min(x),max(x)x_ ,x_ ← (x), (x) in PoptP_opt ; ymin,ymax←min(y),max(y)y_ ,y_ ← (y), (y) in PoptP_opt ; sleft←⌈xmindx⌉,sright←⌈L−xmaxdx⌉,sbottom←⌈ymindy⌉,stop←⌈W−ymaxdy⌉s_left← x_ dx ,\;s_right← L-x_ dx ,\;s_bottom← y_ dy ,\;s_top← W-y_ dy Xshift←−sleft,…,sright⋅dxX_shift←\-s_left,…,s_right\· dx ; Yshift←−sbottom,…,stop⋅dyY_shift←\-s_bottom,…,s_top\· dy ; Pext←(x+δx,y+δy)|(x,y)∈Popt,δx∈Xshift,δy∈YshiftP_ext←\(x+ _x,\ y+ _y)\ |\ (x,y)∈ P_opt,\ _x∈ X_shift,\ _y∈ Y_shift\ // 3. Radius computation and FoV-intersection filtering PPA←fPPA(w∗)PPA← f_PPA(w ) ; r←PPA/πr← PPA/π ; // Shoot dry weight--PPA mapping step Pvalid←(x,y)∈Pext∣−r≤x≤L+r,−r≤y≤W+rP_valid←\(x,y)∈ P_ext -r≤ x≤ L+r,\ -r≤ y≤ W+r\ ; Pfinal←unique(Pvalid)P_final (P_valid) ; // 4. Canopy layout construction ←Circle(x,y,r)|(x,y)∈PfinalC←\Circle(x,y,r)\ |\ (x,y)∈ P_final\ ; return C 2.1.3 Unity rendering engine The Unity rendering engine generates synthetic top-view RGB images together with corresponding binary segmentation masks, by capturing the reconstructed canopy appearance using a virtual camera. The canopy appearance is reconstructed from the canopy layout representation. As illustrated in Fig. 2, the rendering engine operates in two steps: scene initialisation and scene update. Scene initialisation is performed prior to simulation, using the initial configuration provided as inputs. The FoV of 1m21~m^2 is initialised as a rectangular domain of L×WL× W. The virtual camera is configured with a user-specified image resolution. A top-down orthographic projection is used to generate the top-view images, which preserves a consistent pixel-to-metric scaling across the FoV and eliminates perspective distortion. The scene update is performed at each image sampling time step, after the canopy layout representation has been generated by the canopy layout algorithm. The previously generated canopy layout representation and the simulated day tdayt_day are taken as input in order to construct the canopy appearance. The update process consists of two stages: individual plant updating and overall canopy reconstruction. For individual plant updating, lettuce morphological development is approximated by a simple rule: each seedling has three leaves at transplanting, the leaf number increases by one per day, and is capped at 34 leaves (i.e., when tday≥30t_day≥ 30). Based on this rule, a library of 31 prefabricated lettuce models was constructed in Blender, each representing a specific leaf number from 3 to 34. Leaves were sampled from real leaf images that covered all growth stages, and each model was constructed by stacking leaves with their tips arranged in a spiral around the centroid. For a given tdayt_day, the corresponding prefab is selected and scaled uniformly in all three dimensions by means of using the radius parameter r in C. When desired, a small random in-plane rotation and a scale perturbation can be applied per plant instance to introduce limited plant-level variability. The canopy appearance is then constructed by placing the selected and scaled prefabs within the FoV according to the final plant positions PfinalP_final in C. Each prefab is positioned by aligning the centre of its base with the corresponding coordinates. Finally, the updated scene is rendered by the virtual camera, which outputs the corresponding top-view RGB image and binary segmentation mask. Figure 2: Overview of two steps in the Unity rendering engine for synthetic image generation. Scene initialisation uses predefined configurations to initialise the scene prior to simulation. Scene updates reconstruct the canopy appearance based on the canopy layout representation, from which synthetic RGB and segmentation images are rendered with a virtual camera. 2.2 Data acquisition This section introduces the datasets used for developing and validating LettuceVisSim. The Data description section details two publicly available datasets, their experimental setups, and the types of data collected. The Data Selection and Processing section outlines the steps taken to ensure consistency in cultivar selection, image quality, and preprocessing for extracting relevant features for development and validation. 2.2.1 Data description Publicly available datasets from the 3rd Autonomous Greenhouse Challenge were used in this study. The datasets were collected during lettuce cultivation experiments conducted in Bleiswijk, The Netherlands, in 2021 and 2022. Specifically, two datasets with different experimental setups were used, and they are briefly described below. Detailed protocols are provided in the original publications. Dataset (i) This dataset, collected in 2021, comprises top-view RGB-D images of individual lettuce plants from four cultivars, including cv. Lugano, spanning a range of developmental stages from seedling to harvest. Each plant image is paired with its corresponding shoot dry weight wiw_i and additional phenotypic traits [Hemming et al., 2021]. Dataset (i) This dataset was collected in February–March and May–June 2022, during two cultivation cycles of cv. Lugano, each under 6 distinct cultivation strategies, yielding 12 strategies in total. This dataset comprises hourly top-view RGB-D time-series images of lettuce canopy over an area of 1 m2m^2. In addition to image data in dataset (i), synchronised environmental and management records were collected, together with weekly destructive dry weight measurements [Petropoulou et al., 2023]. Specifically, the multimodal time-series dataset across 12 cultivation strategies, including canopy images, climate variables, spacing management records, and shoot dry weight measurements, was used in this study. A summary of the environmental conditions and strategy abbreviations, which refer to the participating team name and cultivation cycle, is provided in Table 1. Table 1: Summary of realised indoor climate variables for all teams across two cultivation cycles. Min and Max denote the minimum and maximum recorded values, and SD denotes the standard deviation Cultivation cycle Team Air remperature (°C) Indoor radiation (W m-2) Carbon dioxide concentration (ppm) Abbreviation Min Mean ± SD Max Min Mean ± SD Max Min Mean ± SD Max 2 February to March 2022 cva 12.60 20.05± 3.67 30.20 0 19.24± 26.47 114.62 408.00 489.00± 117.35 974.00 cva1 koala 11.20 19.63± 3.36 28.40 0 40.76± 24.92 96.79 399.00 811.01± 233.54 1279.00 koala1 monday-lettuce 15.30 21.88± 3.26 29.60 0 33.92± 34.68 114.84 361.00 704.97± 218.26 1568.00 monday-lettuce1 digital-cucumbers 15.50 19.78± 2.03 29.10 0 26.43± 25.32 100.92 501.00 919.74± 95.04 1780.00 digital-cucumbers1 veggie-might 10.10 19.80± 3.63 30.60 0 36.49± 25.37 107.66 415.00 667.48± 119.05 906.00 veggie-might1 reference 12.00 17.87± 2.90 29.20 0 22.61± 18.03 90.92 393.00 596.26± 75.73 1067.00 reference1 4 May to June 2022 cva 12.90 19.63± 4.05 31.60 0 31.16± 44.38 383.45 383.00 547.45± 158.26 1338.00 cva2 koala 11.70 20.17± 3.57 30.80 0 32.99± 46.69 373.23 360.00 463.00± 83.74 1123.00 koala2 monday-lettuce 13.90 21.67± 4.00 32.40 0 27.20± 32.04 359.09 330.00 488.68± 142.22 1025.00 monday-lettuce2 digital-cucumbers 17.00 22.48± 3.25 36.70 0 26.55± 47.18 382.15 427.00 757.95± 179.11 1329.00 digital-cucumbers2 veggie-might 14.10 20.49± 3.54 31.20 0 44.51± 69.04 372.14 385.00 486.11± 71.07 1085.00 veggie-might2 reference 13.90 21.23± 3.84 32.40 0 27.95± 33.91 359.09 330.00 495.55± 137.72 1012.00 reference2 2.2.2 Data selection and processing Selection was applied to both Dataset (i) and Dataset (i) for two purposes. First, the selection ensured that both datasets finally contained growth measurements of the same lettuce cultivar, thereby supporting cultivar-consistent growth modelling and cross-dataset validation. Second, the selection guaranteed that crop pixels were clearly captured in the images, allowing extraction of image-based features. Dataset (i) Only images and corresponding measurements of cv. Lugano were used. After selection, images were processed to extract PPA. As exemplified in Fig. 4(A), the lettuce plants in each image were first segmented manually from the background using the Segment Anything Model [Kirillov et al., 2023]. The minimum enclosing circle of each segmented lettuce region was then computed, together with the pixel count inside the circle. The physical area of the circle was obtained from the measured plant diameter, and the PPA of image j, denoted (PPAjPPA_j) was estimated via the resulting pixel-to-area mapping. This process yielded 96 pairs of shoot dry weight and PPA measurements, defined as the dataset: i=(wj,PPAj)j=1N=96D^i=\(w_j,\,PPA_j)\_j=1^N=96 (3) Dataset (i) Images were first screened based on illumination conditions. Only images captured during periods in which the indoor photosynthetically active radiation exceeded 5 μmol m−2 s−1 m^-2 s^-1 were included, ensuring that canopy was clearly visible in the images, as shown in Fig. 3. After applying this threshold, approximately 40% (4942 images) of the original images were retained. Figure 3: Illustrative examples of image screening based on illumination conditions in Dataset (i). From left to right: a representative image with good canopy visibility (indoor photosynthetically active radiation above 5 μmol m−2 s−1 m^-2 s^-1), an image captured when illumination was lower than the threshold, and an image captured under purely dark conditions. After selection, images were processed to estimate GCR, following the protocol of Petropoulou et al. [2023]. Images were first sampled from all cultivation strategies at fixed 7-day intervals, starting from the first day of each cultivation cycle. For each sampling day, two images were selected at 09:00 and 16:00 to capture canopy appearance under stable morning and afternoon lighting conditions prior to annotation. This sampling procedure yielded 131 canopy images for annotation, in which all lettuce plants with visually distinguishable boundaries were manually labelled, as exemplified in Fig. 4(B). After annotation, the images were split randomly into training, validation, and test sets in a 6:2:2 ratio and used to train a DeepLabv3+ model [Chen et al., 2018] for semantic segmentation, following the same approach as Petropoulou et al. [2023]. A mean intersection over union (mIoU, Eq. (27)) of 93.5% was achieved on the test set (B). Compared to Petropoulou et al. [2023], who used 23 annotated images for training and 12 for validation, this study used substantially more annotated samples, providing a stronger basis for model training. Once trained, the model was applied to all remaining selected images in Dataset (i) to generate the corresponding segmentation masks. For each generated mask, as exemplified in Fig. 4(C), GCR was computed as the ratio of the number of pixels classified as canopy to the total number of pixels, which yielded a GCR time series. Figure 4: Examples of image annotation and predicted masks across different datasets. (A) Annotation of lettuce plants and visualisation of their minimum enclosing circles in Dataset (i); (B) annotation of lettuce plants within the canopy of Dataset (i); (C) corresponding predicted masks generated by the trained DeepLabv3+ model from the input images shown in panel (B). Beyond GCR estimation, these annotated images were also used to quantify the number of lettuce plants visible within the camera field of view. Because the original plant density records pdtpd_t were available only at a daily resolution, hourly measured time-series images were additionally inspected to determine density changes based on temporal canopy development, which enables simulation at shorter time intervals. The relation between pdtpd_t and the visible plant counts derived from the annotated images is given in C. In addition to these image-derived quantities, the weekly destructive shoot dry weight measurements from Dataset (i) are formally defined as: i=ws,t∣s∈,t∈s,D^i=\\,w_s,t s ,\;t _s\,\, (4) where S denotes the set of 12 cultivation strategies and sT_s denotes the set of destructive sampling time points for strategy s. Hence, ws,tw_s,t is the shoot dry weight of cultivation strategy s at time t. 2.3 Experiment description This section describes the experimental procedures used to develop, validate, and evaluate the LettuceVisSim. Experiment 1 examined whether the PBM, originally developed under a fixed plant density, remained valid for predicting shoot dry weight dynamics under dynamic plant-density management. Experiment 2 compared regression models for mapping shoot dry weight to PPA and selected the best-performing model for the canopy layout algorithm. Experiment 3 validated the canopy layout representation by comparing simulated GCR dynamics with those estimated from measured images under varying environmental and spacing conditions, considering both measured and PBM-simulated shoot dry weight as inputs. Experiment 4 evaluated the Unity rendering engine in terms of output diversity and computational efficiency for synthetic image generation. In Experiment 5, a proof of concept of vision-based RL with LettuceVisSim was provided. 2.3.1 Experiment 1: validation of the process-based model under dynamic plant-density management In Experiment 1, the PBM (Section 2.1.1) for shoot dry weight prediction under dynamic plant-density management was validated with the measured shoot dry weight iD^i (Eq. (4)) and the synchronised environmental and plant-density records of the 12 strategies in S (Table 1). A six-fold leave-strategy-out cross-validation was used to evaluate the PBM on strategies not seen during calibration [Roberts et al., 2017]. First, the 12 strategies in S were split randomly into six folds of two strategies each. Second, the following steps were performed in each run k (k=1,…,6k=1,…,6): 1. One fold served as the held-out test set testkS_test^k and the other five as the training set trainkS_train^k. 2. In the calibration step, the optimisation in (5) was solved. 3. In the evaluation step, the trained model was tested on testkS_test^k. In the calibration step, based on the sensitivity analysis of the PBM [Van Henten and Van Straten, 1994], only the five parameters most influential for biomass accumulation, pcal=(cb,ce,cgr,max,cK,clar)Tp_cal=(c_b,\ c_e,\ c_gr,max,\ c_K,\ c_lar)^T, were calibrated, with the remaining parameters held fixed at their original values (A). A parameter set pcalp_cal was estimated by running the PBM (Eq. (2)) forward over the training strategies and minimising the squared error between the simulated shoot dry weight w^s,t(pcal) w_s,t(p_cal) and the measured shoot dry weight ws,tw_s,t, pcal,k∗=argminpcal∑s∈traink∑t∈s(w^s,t(pcal)−ws,t)2,p_cal,k = _p_cal _s _train^k _t _s ( w_s,t(p_cal)-w_s,t )^2, (5) where ws,t∈iiw_s,t ^i and sT_s are the destructive sampling times (Eq. (4)). The optimisation was carried out with the scipy.optimize module of SciPy. In the evaluation step, the calibrated PBM was run forward on each of the two strategies s∈testks _test^k to produce two shoot dry weight trajectories, and the six runs together yielded 12 test trajectories. Performance was computed by comparing simulated shoot dry weights with the corresponding measurements. It was quantified by the coefficient of determination (R2R^2), measuring how well the simulation captured the observed variation in shoot dry weight, and the relative root mean squared error (RRMSE), preferred over absolute error because shoot dry weight spans a wide range across growth stages and strategies. Both are defined in D and reused in the subsequent experiments. These metrics were computed at both the fold and strategy levels. At the fold level, the two held-out strategies in each testkS_test^k were pooled to obtain one R2R^2 and one RRMSE, as is commonly done in crop model studies [Droutsas et al., 2022, Hussain et al., 2026]. At the strategy level, the two metrics were instead computed on each of the 12 test trajectories separately. This strategy-wise reporting keeps poorly fitted strategies from being hidden by pooling and offers a more complete view of model performance [Bates et al., 2024]. The same 12 test trajectories were subsequently used as the PBM-driven shoot dry weight inputs to the canopy layout algorithm in Experiment 3. 2.3.2 Experiment 2: model selection for the shoot dry weight–PPA mapping Experiment 2 compared regression models and selected the one used to serve as fPPAf_PPA in the simulator. Specifically, this comparison considered a set of one-phase regression models, and a two-phase piecewise cubic regression was included as the proposed approach. The model formulations are given below. One-phase models: Shoot dry weight is mapped to PPA by a single function over the entire shoot dry weight range, Linear:y(w∗) :~~y(w ) =βlinw∗+αlin, = _lin\,w + _lin, (6) θlin _lin =(βlinαlin)T. = pmatrix _lin& _lin pmatrix^T. Quadratic:y(w∗) :~~y(w ) =β2quad(w∗)2+β1quadw∗+αquad, = _2^quad(w )^2+ _1^quadw +α^quad, (7) θquad _quad =(β2quadβ1quadαquad)T. = pmatrix _2^quad& _1^quad&α^quad pmatrix^T. Cubic:y(w∗) :~~y(w ) =β3cub(w∗)3+β2cub(w∗)2+β1cubw∗+αcub, = _3^cub(w )^3+ _2^cub(w )^2+ _1^cubw +α^cub, (8) θcub _cub =(β3cubβ2cubβ1cubαcub)T. = pmatrix _3^cub& _2^cub& _1^cub&α^cub pmatrix^T. Quartic:y(w∗) :~~y(w ) =β4qr(w∗)4+β3qr(w∗)3+β2qr(w∗)2+β1qrw∗+αqr, = _4^qr(w )^4+ _3^qr(w )^3+ _2^qr(w )^2+ _1^qrw +α^qr, (9) θqr _qr =(β4qrβ3qrβ2qrβ1qrαqr)T. = pmatrix _4^qr& _3^qr& _2^qr& _1^qr&α^qr pmatrix^T. Logistic:y(w∗) :~~y(w ) =Llog1+e−klog(w∗−w0,log), = L_log1+e^-\,k_log\,(w -w_0,log), (10) θlog _log =(Llogklogw0,log)T. = pmatrixL_log&k_log&w_0,log pmatrix^T. Hyperbolic:y(w∗) :~~y(w ) =ahypw∗−w0,hyp+bhyp, = a_hyp\,w -w_0,hyp\,+b_hyp, (11) θhyp _hyp =(ahypw0,hypbhyp)T, = pmatrixa_hyp&w_0,hyp&b_hyp pmatrix^T, Two-phase model: Because the relation between shoot dry weight and PPA may vary, a piecewise cubic regression is proposed. It is composed of two cubic polynomial segments, f1f_1 and f2f_2, joined at a breakpoint wbw_b, with continuity in both the function value and the first derivative, Piecewise:y(w∗) :~~y(w ) =f1=a01+a11w∗+a21(w∗)2+a31(w∗)3,w∗<wb,f2=b02+b12w∗+b22(w∗)2+b32(w∗)3,w∗≥wb, = casesf_1=a_0^1+a_1^1w +a_2^1(w )^2+a_3^1(w )^3,&w <w_b,\\ f_2=b_0^2+b_1^2w +b_2^2(w )^2+b_3^2(w )^3,&w ≥ w_b, cases (12) subject to to f1(wb)=f2(wb), f_1(w_b)=f_2(w_b), f1′(wb)=f2′(wb). f_1 (w_b)=f_2 (w_b). with θpw=(a01a11a21a31b02b12b22b32)T _pw= pmatrixa_0^1&a_1^1&a_2^1&a_3^1&b_0^2&b_1^2&b_2^2&b_3^2 pmatrix^T the parameter vector that has been optimised. This approach is intended to capture the early and late growth stages, separately. The prime symbol (′) denotes the derivative with respect to w∗w . Note again that w∗=w =w when measured shoot dry weight is used and w∗=w^w = w when shoot dry weight simulated by PBM, (Eq. (2)) is used Experiment 2 was conducted on paired shoot dry weight–PPA dataset iD^i (Eq. (3)) with five-fold cross-validation. This procedure was used to compare candidate model structures and breakpoint settings. The set iD^i was sorted in ascending order of shoot dry weight and partitioned into five folds, ensuring that the full biomass range was represented in each fold. In the kthk^th cross-validation run, four folds formed the training set train,kiD^i_train,k, while the remaining fold formed the held-out test set test,kiD^i_test,k. For a given regression model y(⋅,θm)y(·; _m) for m=lin,quad,cub,qr,log,hyp,pwm=\lin,quad,cub,qr,log,hyp,pw\, this procedure was repeated for all five folds, such that each fold served once as the test set. The model parameters in each run were estimated by using scipy.optimize module in SciPy to minimise the sum of squared residuals on the training set, θ^m(k)=argmin∑j∈train,kiθm(PPAj−y(wj,θm))2, θ_m^(k)= _ _m _j ^i_train,k (PPA_j-y(w_j; _m) )^2, (13) where θ^m(k) θ_m^(k) denotes the estimated parameters of the model in the kthk^th run. For all one-phase models (m≠pwm ), parameters were estimated using the full training set. For the two-phase model (m=pwm=pw), the parameters of each segment were estimated on the corresponding sub-range of the training set, the parameters of f1f_1 on training samples with w<wbw<w_b, and the parameters of f2f_2 on training samples with w≥wbw≥ w_b, subject to the continuity conditions in Eq. (12). The fitted model’s predictive performance was then calculated from test,kiD^i_test,k using each θ^m(k) θ_m^(k) for k=1,…,5k=1,…,5. Predictive performance was quantified with the same R2R^2 and RRMSE metrics introduced in Experiment 1, here applied to PPA and summarised over the five folds. The proposed two-phase model was first compared with the one-phase models with a fixed breakpoint wb=0.7gw_b=0.7~g. Performance was evaluated over the entire shoot dry weight range, as well as separately for samples with w<wbw<w_b and w≥wbw≥ w_b in order to examine stage-specific fitting behaviour. The sensitivity of model performance to breakpoint selection was then assessed by varying wbw_b from 0.30.3 to 1.1g1.1~g in increments of 0.2g0.2~g. For each candidate breakpoint, the two-phase model was fitted and evaluated with the same cross-validation procedure. Based on cross-validation results, the model with the best overall performance was selected. The selected model was then refitted on the complete dataset iD^i with the same least-squares fitting procedure as described above, i.e., θ^m∗=argmin∑j∈iθm(PPAj−y(wj,θm))2. θ_m^*= _ _m _j ^i (PPA_j-y(w_j; _m) )^2. (14) Here, θ^m∗ θ_m^* is subsequently used in Experiment 3 to construct the canopy layout representation, which is evaluated on Dataset (i). Dataset (i) was collected independently, in a different experiment from Dataset (i). 2.3.3 Experiment 3: validation of the canopy layout representation Experiment 3 validated whether the canopy layout representation could reproduce GCR dynamics consistent with those derived from measured images under dynamic environmental and spacing conditions. The representation was driven by two sources of shoot dry weight: (i) the measured shoot dry weight, which isolates the validity of the representation itself under accurate inputs, and (i) the PBM-simulated shoot dry weight from Experiment 1, which reflects the downstream GCR agreement obtained when the representation is driven by model-predicted rather than measured inputs. The simulated GCR was derived from the canopy layout representation with a common representation-to-GCR conversion procedure in both cases. The shoot dry weight input w∗w and the corresponding plant density pdtpd_t were used as inputs to the canopy layout algorithm to generate a canopy layout representation, which was then converted into a binary mask at the same image resolution as the measured images (1920×10801920× 1080), using the pixel-to-metric scaling of the field of view. This ensured consistency with the GCR estimation method applied to measured images. Pixels were marked as covered if their squared Euclidean distance to the nearest plant centre was less than or equal to the squared canopy radius r, and the GCR was calculated from the resulting binary mask. Agreement between simulated and image-derived GCR was quantified using R2R^2 and RRMSE. For the validation driven by measured shoot dry weight, the measured shoot dry weight w and the corresponding plant density were used as w∗w and pdtpd_t. Because shoot dry weight was obtained by destructive sampling, this comparison was performed only on the days for which destructive measurements were available, and the simulated GCR was compared against the daily averaged image-derived GCR on those days. The daily reference GCR was obtained by averaging the image-derived GCR values from all observations on the same day, with the standard deviation used to characterise within-day variability. For the validation driven by PBM-simulated shoot dry weight, the test-strategy dry weight trajectories w^t w_t from the six-fold leave-strategy-out cross-validation in Experiment 1, together with the corresponding plant density records pdtpd_t, were used as w∗w and pdtpd_t to generate time series of canopy layout representations, from which GCR time series were derived. The resulting GCR time series were compared with the hourly image-derived GCR at matched time points. 2.3.4 Experiment 4: evaluation of the Unity rendering engine This experiment evaluated the proposed Unity rendering engine in terms of output diversity under different rendering configurations and computational efficiency. The evaluations were conducted under a simulation scenario considering a 30-day cultivation period using real climate and plant spacing records from strategy cva1. To demonstrate the ability of the engine to generate diverse visual outputs, identical simulation states were rendered under different configurations, including varying lighting levels, image resolutions, and randomised plant rotations using the selected prefabs. Computational efficiency was quantified by the average computation time per frame, defined as the total wall-clock time divided by the number of generated frames, and assessed in two steps. First, the cost of individual stages was analysed by incrementing the execution scope: the PBM only, the PBM plus the canopy layout algorithm, and the full pipeline. For this analysis, the canopy layout representation was converted into a binary mask at an image resolution of 256×256256× 256 pixels with three image sampling intervals (5 min, hourly and daily), while rendered images were generated with a square field of view (L=W=1L=W=1 m) and an image resolution of 256×256256× 256 with two image sampling intervals (hourly and daily). Second, the full pipeline was evaluated under varying image sampling intervals (hourly and daily) and image resolutions (84×8484× 84 to 1920×10801920× 1080). For each configuration, five independent runs were conducted to account for runtime variability. 2.3.5 Experiment 5: proof of concept of vision-based reinforcement learning with LettuceVisSim Experiment 5 provided a proof of concept of the simulator for vision-based RL in a vertical farming control problem, in which crop growth is controlled by optimising the light based on crop image observations. The set-up is described below. Control task A light-intensity control task over a fixed cultivation horizon of H=30H=30 days is considered. The control objective is to steer the terminal shoot dry weight w^H w_H into a harvest band of [15,17]g⋅plant−1[15,17]~g·plant^-1 while keeping the biomass trajectory non-decreasing throughout the cycle. Shoot dry weight accumulation is simulated by the PBM (Section 2.1.1), which updates the per-plant shoot dry weight w^d w_d on day d in response to the environmental inputs and a daily lighting setpoint. At the start of each day d∈0,…,H−1d∈\0,…,H-1\, the vision-based RL agent observes a crop image and, based on it, calculates a lighting setpoint ad∈[0,360]μmol⋅m−2⋅s−1a_d∈[0,360]~ ·m^-2·s^-1, expressed as a photosynthetic photon flux density (PPFD). This is then applied as incident radiation during the 18 h photoperiod and set to zero otherwise. Throughout the cultivation, air temperature is set to 22∘22~ C during the light period and 20∘20~ C during the dark period. The CO2 concentration is held constant at 800800 ppm, and plant density is fixed at 18plants⋅m−218~plants·m^-2. Image observation At each day, the vision-based RL agent received a top-view canopy RGB image of 84×8484× 84 resolution as its sole observation and computed the lighting decision at a daily interval. Reward and PPO agent The reward function R(w^d)R( w_d) combines a dense per-day term with a sparse terminal term, which encourages the terminal shoot dry weight to land within the harvest band, while keeping the trajectory non-decreasing, R(w^d)=w^d−w^d−1,w^d−w^d−1≥0,d<H,−5,w^d−w^d−1<0,d<H,10,w^H∈[smin,smax],d=H,−10|w^H−smin+smax2|,otherwise,d=H,R( w_d)= cases w_d- w_d-1,& w_d- w_d-1≥ 0,\;\;d<H,\\ -5,& w_d- w_d-1<0,\;\;d<H,\\ 10,& w_H∈[s_ ,s_ ],\;\;d=H,\\ -10\, | w_H- s_ +s_ 2 |,&otherwise,\;\;d=H, cases (15) where [smin,smax]=[15,17]g⋅plant−1[s_ ,s_ ]=[15,17]~g·plant^-1 is the harvest band defined above. The first two terms return the one-day biomass gain and penalises any decrease in shoot dry weight, whereas the last two terms reward landing inside the harvest band and otherwise penalises the deviation from the band centre. Proximal Policy Optimization (PPO) [Schulman et al., 2017] was used as the vision-based RL algorithm in this demonstration, with an asymmetric actor–critic architecture: a convolutional encoder maps the image observation to the actor, which therefore depends on the image alone, while the critic additionally receives the shoot dry weight during training to stabilise value estimation. This keeps the deployed policy dependent on vision only. The network architecture and full PPO hyperparameters are detailed in E. 2.3.6 Experiment environment All experiments were conducted on a Lenovo ThinkPad P15 Gen 2i laptop equipped with an Intel Xeon W-1885M CPU (12 cores, 3.2 GHz), 32 GB RAM, and an NVIDIA RTX A5000 laptop GPU (16 GB VRAM), running Pop!_OS (64-bit). The simulation and data analysis were implemented in Python 3.10, using NumPy 1.26, OpenCV 4.9, PyTorch 2.0 and SciPy 1.15.3. The rendering engine was built in Unity (version 6000.0.48f1) and was executed in headless mode for automated simulation rendering. 3 Results 3.1 Experiment 1 Table 2 shows the fold-wise performance for PBM shoot dry weight prediction, for the training and test folds in each cross-validation run. Averaged over the six folds, the train agreement was R2=0.873±0.031R^2=0.873± 0.031 (RRMSE 37.6±4.9%37.6± 4.9\%) and the test agreement was R2=0.836±0.131R^2=0.836± 0.131 (RRMSE 38.6±17.1%38.6± 17.1\%), which indicates comparable agreement on the train and test strategies. Across folds, the train agreement stayed within a narrow range (R2R^2 from 0.8310.831 to 0.9210.921), whereas the test agreement varied much more widely (R2R^2 from 0.6240.624 to 0.9550.955). A similar pattern was observed for RRMSE: the train RRMSE remained within a narrow range (29.5%29.5\% to 43.7%43.7\%), whereas the test RRMSE spanned a much wider range (20.5%20.5\% to 70.0%70.0\%). The lowest test agreement occurred in Fold 5 (veggie-might1, koala2), with the lowest test R2R^2 (0.6240.624) and the highest test RRMSE (70.0%70.0\%) among all folds. Table 2: Fold-wise performance of the six-fold leave-strategy-out cross-validation for shoot dry weight prediction by the process-based model, R2R^2 denotes the coefficient of determination, RRMSE the relative root mean squared error and SD the standard deviation. Fold Test strategies Train Test R2R^2 RRMSE R2R^2 RRMSE 1 cva2, veggie-might2 0.831 43.7% 0.955 20.5% 2 koala1, monday-lettuce2 0.896 35.1% 0.683 52.2% 3 digital-cucumbers1, reference1 0.866 37.7% 0.911 32.2% 4 monday-lettuce1, reference2 0.864 39.4% 0.925 27.6% 5 veggie-might1, koala2 0.921 29.5% 0.624 70.0% 6 cva1, digital-cucumbers2 0.858 40.3% 0.916 29.4% Mean ± SD 0.873 ± 0.031 37.6 ± 4.9% 0.836 ± 0.131 38.6 ± 17.1% Whereas Table 2 summarises agreement at the fold level, Fig. 5 unpacks the same cross-validation into the 12 per-strategy test trajectories, each generated using the fold-specific parameters from the cross-validation run in which that strategy was held out. The simulated trajectories followed the general growth trend in most strategies, with fold-wise test R2R^2 ranging from 0.6240.624 to 0.9550.955 (Table 2) and test R2≥0.91R^2≥ 0.91 in four of the six folds. The largest deviation occurred in veggie-might1, where the simulated shoot dry weight became much higher than the measured values at the late growth stage. Figure 5: Shoot dry weight simulated by the process-based model (PBM) for the 12 cultivation strategies. For each strategy, the trajectory was generated with the parameter set calibrated on the cross-validation fold in which that strategy was held out, so every trajectory shown is an out-of-sample prediction. One timestep corresponds to 5 min. Blue lines denote the simulated shoot dry weight and red circles the destructively measured shoot dry weight. The corresponding per-strategy metrics are listed in Table 1. 3.2 Experiment 2 Table 3 summarises the cross-validation performance of the proposed two-phase regression model with wb=0.7gw_b=0.7~g against the one-phase regression models. Overall, the two-phase model yielded best average performance across five folds (R2=0.94R^2=0.94, RRMSE==22%), though cubic and quartic models achieved near-identical overall metrics with overlapping fold-level standard deviations. Stage-wise results revealed that the clearest advantage of the two-phase model appeared in the early stage (w<wbw<w_b), where it achieved R2=0.78R^2=0.78 and RRMSE==29% while most one-phase models degraded substantially. In the late stage (w≥wbw≥ w_b), model performance became closer, and the two-phase model remained competitive with the top one-phase models. Table 3: Comparison of one-phase and two-phase regression models for potential projected area (PPA) prediction across the overall dataset, the early stage (w<0.7gw<0.7\,g) and the late stage (w≥0.7gw≥ 0.7\,g). Values are reported as mean values over five cross-validation folds, with standard deviations given in parentheses. Type Model Overall Early stage Late stage R2R^2 RRMSE R2R^2 RRMSE R2R^2 RRMSE One-phase lin 0.91 (0.04) 28 (4.08)% -0.27 (0.29) 70 (8.41)% 0.82 (0.10) 21 (3.71)% quad 0.92 (0.02) 25 (2.93)% 0.46 (0.08) 45 (4.60)% 0.84 (0.07) 20 (2.64)% cub 0.94 (0.02) 23 (2.61)% 0.72 (0.05) 33 (3.82)% 0.87 (0.05) 18 (2.36)% qr 0.94 (0.02) 23 (2.73)% 0.74 (0.06) 32 (3.89)% 0.86 (0.05) 19 (2.47)% log 0.89 (0.03) 31 (2.82)% -0.45 (0.30) 74 (8.68)% 0.78 (0.07) 24 (2.55)% hyp 0.93 (0.02) 24 (2.85)% 0.67 (0.05) 36 (3.51)% 0.85 (0.06) 19 (2.58)% Two-phase pw 0.94 (0.02) 22 (2.90)% 0.78 (0.04) 29 (3.02)% 0.87 (0.05) 18 (2.57)% Note: Mean value and standard deviations (in parentheses) are reported. Bold values indicate the best performance within each column, defined as the highest R2R^2 and the lowest RRMSE. Model abbreviations are consistent with the m notation defined in Section 2.3.2: lin (linear), quad (quadratic), cub (cubic), qr (quartic), log (logistic), hyp (hyperbolic) and pw (piecewise). Fig. 6 illustrates the sensitivity of R2R^2 to the breakpoint wbw_b (from 0.30.3 to 1.1g1.1~g). Although the overall R2R^2 remained relatively insensitive to wbw_b, the highest overall R2R^2 of 0.940.94 was consistently achieved by the two-phase model across the evaluated breakpoint range, which exceeded all one-phase models (Fig. 6(a)). By contrast, the stage-specific trends responded differently to a change in breakpoint (Fig. 6(b)): the early-stage performance improved with larger wbw_b, stabilising around wb=0.7gw_b=0.7~g, whereas late-stage performance decreased monotonically as wbw_b increased. Figure 6: Left: Comparison of overall R2R^2 between one-phase models and the two-phase model for describing the relationship between PPA and shoot dry weight, with the two-phase model evaluated across candidate breakpoints (wb=0.3w_b=0.3–1.1g1.1\,g). Right: Changes in R2R^2 for the early and late stages of the two-phase model across the same breakpoint range. All values represent the average performance over five-fold cross-validation. On the basis of the results above, two-phase model was selected and wb=0.7w_b=0.7 g was identified as a conservative breakpoint for subsequent analyses. This value corresponds to the smallest breakpoint at which early-stage performance stabilises, without compromising late-stage performance. The final fPPAf_PPA used in subsequent experiments takes the form, fPPA(w∗,θpw)=10−31.444+13.444w∗−3.336(w∗)2−1.767(w∗)3,w∗<0.7,3.789+7.206w∗−0.592(w∗)2+0.024(w∗)3,w∗≥0.7,f_PPA(w ; _pw)=10^-3 cases1.444+13.444w -3.336(w )^2-1.767(w )^3,&w <0.7,\\ 3.789+7.206w -0.592(w )^2+0.024(w )^3,&w ≥ 0.7, cases (16) in which fPPAf_PPA is expressed in m2 and w∗w in g plant-1. The optimised (rounded) parameter vector is θpw=10−3×(1.44413.444−3.336−1.7673.7897.206−0.5920.024)T _pw=10^-3× pmatrix1.444&13.444&-3.336&-1.767&3.789&7.206&-0.592&0.024 pmatrix^T. The shoot dry weight input, corresponding to either the measured shoot dry weight w or the PBM-simulated shoot dry weight w w, as defined in Section 2.1.2. 3.3 Experiment 3 Fig. 7 presents a visual comparison between canopy masks generated from canopy layout representations using measured shoot dry weight as input and canopy masks segmented from measured RGB images on the same day. At early growth stages, the simulated and measured masks showed similar canopy occupancy patterns. As cultivation progressed, structural differences became more visible: the simulated masks retained a more regular grid-based arrangement, whereas the measured masks showed more irregular uncovered areas and plant positions. Figure 7: Visual comparison between binary masks generated from the canopy layout representation, with their RGB images and corresponding masks at different sampling dates from the cva1 strategy. The numbers on the left indicate the corresponding sampling dates. (A) Binary masks derived from the canopy layout representation, simulated using measured shoot dry weight on each sampling date. (B) Measured RGB canopy images acquired at 12:00 on the same dates, and (C) the corresponding binary masks segmented using the trained DeepLabv3+. Fig. 8 presents the quantitative comparison between GCR simulated from measured shoot dry weight and GCR derived from same-day images across 12 strategies. Overall agreement was strong, with R2=0.84R^2=0.84 and RRMSE ranging from 4.2% to 36.3%. Most strategies showed close agreement between simulated and observed daily GCR. The main exception was observed in strategy veggie-might1, where a large deviation appeared after day 20, resulting in a negative R2R^2 and the largest RRMSE. Excluding this strategy increased the overall performance to R2=0.93R^2=0.93, with a mean RRMSE of 9.4%. Figure 8: Ground coverage ratio (GCR) simulated using measured shoot dry weight across cultivation strategies. Simulated GCR (blue) is compared with the daily averaged image-derived GCR measurements (red), with error bars indicating the standard deviation across observations from the same day. The per-strategy metrics are listed in Table 2. Fig. 9 presents the comparison between GCR simulated from the PBM-simulated shoot dry weight of Experiment 1 and GCR derived from images across the 12 strategies. Because each input trajectory was generated using PBM parameters calibrated without it, this comparison tests the full pipeline on data that the pipeline had not seen during calibration. Averaged across strategies, the agreement was R2=0.40R^2=0.40 with mean RRMSE of 16.8%, substantially lower than that obtained when the representation was driven by measured shoot dry weight. This lower average was, however, driven mainly by a single strategy rather than by a uniform degradation across strategies. Close agreement between simulated and image-derived GCR was still shown by most strategies, and the main temporal trends were reproduced. The main exception was strategy veggie-might1, where a large deviation resulted in a strongly negative R2R^2 (−3.56-3.56) and the largest RRMSE (49.5%). Excluding this strategy increased the average performance to R2=0.76R^2=0.76, with a mean RRMSE of 13.8% and strategy-wise R2R^2 ranging from 0.38 to 0.95, which remained below the corresponding R2=0.93R^2=0.93 achieved under measured shoot dry weight. Among the remaining strategies, koala1 showed the lowest agreement (R2=0.38R^2=0.38, RRMSE 23.0%). Figure 9: Test-strategy Ground coverage ratio (GCR) dynamics across cultivation strategies, simulated using the PBM-simulated shoot dry weight obtained from the six-fold leave-strategy-out cross-validation, with each strategy driven by the fold-specific parameters from the run in which it was held out. Simulated GCR (blue) is compared with image-derived GCR measurements (red). The per-strategy metrics are listed in Table 3. 3.4 Experiment 4 Fig. 10 provides a visual comparison between the rendered and measured top-view RGB images at days 1, 10, 20 and 30. Overall, the major temporal trends were reproduced by the rendered images, including gradual increases in apparent plant size and canopy closure observed in the measurements. Minor discrepancies in spatial arrangement were attributable to the uniform-grid assumption inherent in the canopy layout representation. Figure 10: Visual comparison between rendered and measured RGB images at Days 1, 10, 20, and 30 (12:00) during cultivation. Measured images were obtained from the cva1 strategy, and rendered images were generated from canopy layout representations driven by measured shoot dry weight on the corresponding days. The rendering engine used an aspect ratio of 16:9 and an image resolution of 1920×10801920× 1080, matching those of the measured images. As illustrated in Fig. 11, diverse visual outputs were generated by the rendering engine from an identical canopy layout representation. Variations in illumination and background texture (A–-C) altered the visual style without affecting the underlying geometry, which enables controllable appearance changes while keeping the underlying canopy structure and labels fixed. Conversely, the introduction of plant-level randomisation (D) modified the canopy geometry in a controlled manner, which was accurately reflected in the corresponding segmentation masks. Figure 11: Visual illustration of rendered RGB images and corresponding segmentation masks under different rendering configurations using an identical canopy layout representation. Rendered RGB images (top row) and their corresponding segmentation masks (bottom row) were generated using a fixed square field of view (L=W=1L=W=1 m) and an image resolution of 512×512512× 512. All images were rendered from the same canopy layout representation simulated using the cva1 strategy at day 10. Columns (A)–(C) correspond to low, medium, and high lighting levels, respectively. Column (D) shows an additional configuration with medium lighting combined with randomised prefab scale and rotation. Different background textures were applied across configurations to illustrate visual variation in the rendered outputs. The computational cost of the simulator and of the Unity rendering engine under different configurations is quantified in Fig. 12. As shown in Fig. 12(A), Unity rendering dominated the runtime, whereas the PBM update and canopy layout algorithm contributed substantially less per frame. Moreover, the cost of the canopy layout algorithm increased as the image sampling interval decreased, with 5 min updates requiring more computation than hourly updates. Under daily sampling, Unity rendering engine took approximately four times as long as the canopy layout algorithm. When the sampling interval was reduced from daily to hourly, the rendering time per frame increased by roughly one order of magnitude (about 22 times), while the PBM contribution remained comparatively small. The effect of image resolution is further shown in Fig. 12(B), for both sampling intervals, the average computation time per frame increased with resolution, and this increase was more pronounced under hourly sampling. At the highest tested resolution, the rendering time reached approximately 60 ms per frame under hourly sampling. Figure 12: Comparison of computational efficiency across simulator components and rendering configurations. (A) Average computation time per frame measured under three execution scopes of the simulation pipeline: PBM-only execution, PBM combined with the canopy layout algorithm, and the full pipeline. The canopy layout representation was converted into a binary mask at an image resolution of 256×256256× 256 pixels, while the rendered images were generated with a square field of view (L=W=1 m) and an image resolution of 256×256256× 256 pixels. (B) Average computation time per frame of the full pipeline under different image resolutions and sampling intervals. All simulations were conducted over a 30-day cultivation period, with environmental conditions and plant spacing management of the cva1 strategy as inputs. Each reported value represents the mean of five independent runs; the standard deviation was below 0.005 in all cases and is therefore not shown. 3.5 Experiment 5 It is demonstrated in Fig. 13 that the lighting-control task was learned by the agent directly from images. Training progress is tracked by the accumulated reward, recorded as the running mean of the episode return (Fig. 13(a)), which rose steeply during the early steps and converged after around 100k steps, reaching a maximum episode return of about 5.09. The policy achieving the best accumulated reward was selected for examining the learned behaviour. Fig. 13(b) and (c) show, from a single rollout, the daily lighting action predicted by this policy and the resulting shoot dry weight accumulation across the 30-day cycle, respectively. The shoot dry weight reached 16.1 g⋅plant−1g·plant^-1, within the harvest band. Figure 13: Vision-based reinforcement learning demonstration. (a) Accumulated episode return over training steps, recorded as the running mean of the episode return; the red marker indicates the maximum (max =5.09=5.09). (b) Daily lighting action ada_d predicted by the trained policy. (c) Resulting per-day shoot dry weight trajectory from a single rollout. The shaded band is the harvest band [15,17]g⋅plant−1[15,17]~g·plant^-1. 4 Discussion 4.1 Validation of the process-based model under dynamic plant density Shoot dry weight was predicted reasonably well by the PBM under dynamic plant density in Experiment 1, as supported by the close agreement between the test and the training metrics (R2=0.836±0.131R^2=0.836± 0.131 vs 0.873±0.0310.873± 0.031), which suggests that the calibrated parameters transferred to cultivation strategies not seen during calibration without substantial overfitting. This supports the use of the Van Henten PBM, despite its fixed-density origin, as the upstream growth model for dynamic-spacing scenarios within the scope of the cultivars and conditions examined here. The agreement nonetheless varied across strategies, and this variability was driven by a few difficult strategies rather than by a uniform loss of accuracy, as reflected in the larger spread of the test metrics relative to the train metrics. The clearest example was veggie-might1: the fold containing this strategy showed the weakest test agreement (Table 2). This is also confirmed by the shoot dry weight trajectory in Fig. 5, where veggie-might1 deviated substantially from the measurements during the later growth stage. Because the shoot dry weight that drives the downstream canopy layout representation is provided by the PBM, the accuracy of this upstream prediction directly conditions the validity of the GCR reproduced by the full pipeline, as examined in the following subsections. Two limitations of this evaluation should be noted. First, although the R2R^2 values indicate that the PBM captured the overall shoot dry weight dynamics well, the associated RRMSE values were comparatively large relative to those reported in other lettuce growth modelling studies [Sun et al., 2025]. Such biomass prediction errors may propagate through the downstream pipeline, indicating that the PBM still requires further improvement. Second, the analysis was restricted to a single cultivar; whether the calibrated PBM generalises equally well under dynamic plant density for other cultivars remains to be established. 4.2 Modelling choices for the PPA–shoot dry weight mapping The comparison between the two-phase and one-phase regression models suggests that a stage-dependent strategy better captures the mapping fPPA:w∗PPAf_PPA:w PPA. Although comparable overall cross-validation performance was achieved by several nonlinear one-phase models, the early growth stage (w<wbw<w_b) benefited most from the two-phase formulation. This pattern implies that the relation between PPA and shoot dry weight is not uniform across development, and that the breakpoint wbw_b can be interpreted as a transition point at which the underlying relationship changes. In the context of this study, the value of this mapping lies less in standalone trait prediction than in providing an individual-plant structural parameter with which the canopy layout representation was simulated. From this perspective, improved accuracy at the early growth stage is particularly important. Errors in PPA estimation directly affect the projected canopy radius of individual plants. Under a high plant density, such errors can propagate across many plants when the canopy layout representation is constructed. The better early-stage fit therefore improves the validity of canopy layout representation, rather than merely improving an isolated regression task. The identified breakpoint also implies that the relationship between biomass accumulation and horizontal canopy expansion changes over the course of growth, which is plausible given the shifts in self-shading and rosette expansion that occur as lettuce grows [Geldhof et al., 2021, Liu and Van Iersel, 2022]. In this sense, the two-phase formulation is not only an empirical improvement but also a compact way to reflect a development-dependent change in canopy structure. At the same time, two limitations of the present analysis should be acknowledged. First, the model comparison is based on average cross-validation metrics without statistical testing, so the numerical advantage of the two-phase model over the one-phase models should be interpreted with caution. Second, the proposed mapping was derived from a single lettuce cultivar, whereas previous work has shown that the association between morphological characteristics and shoot dry weight can differ across red and green cultivars [Kim and Van Iersel, 2022]; both the parameter values,and potentially, the functional form of fPPAf_PPA may therefore change for other cultivars. Future work should apply appropriate statistical tests to confirm whether the observed advantage is statistically significant, and should examine whether the two-phase structure remains valid when broader morphological diversity is included. 4.3 Validity of the canopy layout representation The canopy layout representation serves as a structural proxy that links the crop state w∗w to visual observations. Because its construction relies on determining the projection radius r=PPA/πr= PPA/π via the empirical mapping fPPAf_PPA, the validity of the resulting canopy layout representation C depends on whether it preserves canopy-scale structural information consistent with real measurements under dynamic conditions. This validity should be interpreted as functional consistency rather than exact geometric reconstruction. Qualitative comparisons of binary masks (Fig. 7) show that simulated and measured masks were visually similar at early growth stages, whereas more pronounced differences emerged as cultivation progressed: the simulated masks retained a regular grid-based organisation, while the measured masks showed more irregular uncovered gaps, irregular plant positions, and complex canopy boundaries. These discrepancies arise because within-canopy heterogeneity in plant size, shape and local position is neglected by the assumptions of circular canopy projection and uniform spacing. Such variability is instead partially delegated to the rendering stage, where spatial irregularity can be reflected by controlled plant-level randomisation (Fig. 11). When driven by measured shoot dry weight, the image-derived GCR was reproduced closely by the representation, with an overall R2=0.84R^2=0.84 across all strategies which increased to R2=0.93R^2=0.93 when veggie-might1 was excluded. This indicates that the dominant aggregate effects of crop state on canopy coverage are captured by the representation, even though the fine-scale irregularities seen in the masks are not reproduced by its simplified geometry. When instead driven by PBM-simulated shoot dry weight, the GCR agreement decreased to an overall R2=0.40R^2=0.40 that increased to R2=0.76R^2=0.76 when veggie-might1 was excluded (Fig. 9); the representation therefore remained a valid intermediate layer, and its downstream agreement depends on the quality of the input shoot dry weight. Notably, these evaluations were conducted on data independent of those used for calibration, in two senses: (1) the parameters of fPPAf_PPA were estimated on Dataset (i) and validated here on Dataset (i); and (2) in the PBM-driven case, the shoot dry weight trajectories were produced by the leave-strategy-out cross-validation of Experiment 1, so the full pipeline was additionally evaluated on strategies unseen during calibration. Together, these demonstrate the generalisation of the proposed canopy layout representation, both on its own and within the full pipeline, to unseen dynamic environmental and plant-density conditions. The degradation under PBM-simulated shoot dry weight, and its variation across strategies, can be attributed to two stage-dependent error sources. Before canopy closure, the GCR is sensitive to shoot dry weight, so errors in the PBM-simulated shoot dry weight propagate into the GCR; this accounts for most of the gap between the measured- and PBM-driven cases. After canopy closure, however, the GCR saturates and becomes insensitive to shoot dry weight, so the remaining late-stage discrepancy reflects the idealised geometry of the representation rather than the input shoot dry weight: the uniform-grid, circular-overlap construction closes the canopy almost completely, whereas the measured canopy retains the irregular gaps seen in the mask comparison (Fig. 7), leaving the simulated GCR slightly above the measured one. Strategy veggie-might2 illustrates this interaction: although its PBM-simulated shoot dry weight was underestimated at the late growth stage (Fig. 5), the corresponding late-stage GCR was not underestimated but slightly overestimated under both measured and PBM-simulated inputs (Fig. 8 and Fig. 9), consistent with a saturation-dominated, dry-weight-independent error. An exception is koala2, for which the shoot dry weight was predicted accurately yet the downstream GCR agreement still dropped markedly; this exceeds what either error source predicts and points instead to representation-level effects. The results also suggest the boundary conditions of the proposed representation. It is most suitable for highly controlled CEA systems with regular planting layouts and relatively homogeneous canopy development, such as plant factories and high-tech greenhouses. Its validity is limited where canopy development is strongly affected by unmodelled biological or management constraints, or where spatial irregularity plays a larger role. In addition, veggie-might1 not only failed consistently in the shoot dry weight and GCR simulations but also showed a measured GCR that remained below the level reached by most other strategies throughout cultivation, suggesting that canopy development in this strategy may have been restricted by biological or management factors not represented in the current formulation of the canopy layout representation. Another limitation may arise from the simplified imaging assumptions used to derive the simulated GCR. The measured GCR was obtained from real camera images subject to the characteristics of the physical imaging system, whereas the simulated GCR was derived from an idealised canopy layout representation under simplified viewing assumptions. Specifically, the GCR estimated from measured images may be influenced by image-formation factors such as perspective effects, camera intrinsic parameters, lens characteristics, and imperfect alignment between the camera view and the crop rows. None of these factors were modelled explicitly in this study. Consequently, this mismatch between the real imaging process and the idealised representation may contribute to both the visual (Fig. 7) and quantitative (Fig. 9) discrepancies discussed above, adding uncertainty to the validation beyond what the representation alone can account for. This uncertainty is nonetheless unlikely to alter substantially the overall finding that the proposed representation reproduces the dominant canopy-scale trends in GCR dynamics. Taken together, these results support the canopy layout representation as a useful intermediate layer for canopy-scale simulation, while also showing that its validity is conditional rather than universal. Future improvements should therefore proceed along two directions: first, by extending the canopy layout representation to account for environment-dependent structural heterogeneity at the plant level; and second, by designing validation experiments in which camera intrinsic parameters and misalignment between camera view and crop rows are characterised and controlled explicitly, enabling a cleaner separation between representation-level errors and discrepancies arising from image formation effects. 4.4 Implications and future work Taken together, the results of this study suggest that LettuceVisSim constitutes a useful simulator for vision-based RL in CEA. Because biomass dynamics, canopy structure and image generation are represented as connected but modular components, an explicit link, the simulator preserves an explicit link between crop state and visual output while maintaining the computational efficiency required for scalable synthetic data generation. This modular perspective also has methodological implications. Because the PBM, the canopy layout algorithm and the rendering engine are separated but linked, the simulator is easier to interpret, extend and refine. The modular structure also facilitates error attribution: the results of Experiment 3, for example, show that reduced downstream GCR agreement can arise from inaccuracies in upstream shoot dry weight simulation rather than from the canopy layout representation alone. At the same time, the individual components can be replaced or improved without redesigning the full pipeline. A greenhouse crop model such as that of Van Laatum et al. [2025], for instance, could be incorporated in place of the current PBM in order to simulate additional environmental variables simultaneously, which would extend the simulator’s scope to support more complex CEA control problems. Future work should proceed along two main directions. The first concerns further improving simulator accuracy while preserving computational efficiency. This includes extending the shoot dry weight–PPA mapping and canopy layout representation to a broader range of cultivars and environmental conditions, introducing stronger links between environmental dynamics and plant-level structural heterogeneity, improving the treatment of camera alignment and image-formation effects in the validation pipeline, and enriching the prefab library to better represent cultivar-specific appearances and environment-dependent morphological responses. The second direction builds on the present validation to further explore vision-based RL for CEA. It was demonstrated in Experiment 5 that environment control can be learned from crop images by vision-based reinforcement learning. Future studies should extend this towards more realistic settings, including a broader range of control tasks and environmental conditions, comparison with baselines that rely on biomass measurements, and analyses of robustness, generalisation, and sim-to-real transfer. 5 Conclusion This study presents LettuceVisSim, a lettuce growth simulator that closes the data scarcity gap by generating labelled time-series crop images for vision-based RL in CEA. Validated across a broad range of dynamic conditions, the simulator’s capability was established through five main findings. First, validation showed that the PBM predicted shoot dry weight under dynamic plant-density management with R2=0.84R^2=0.84 on unseen cultivation strategies. Second, a two-phase piecewise cubic regression mapped shoot dry weight to PPA with R2=0.94R^2=0.94. Third, the proposed canopy layout representation was shown to be valid under 12 previously unseen cultivation strategies, while its performance depends on the quality of the supplied shoot dry weight, R2=0.84R^2=0.84 when driven by measured values vs R2=0.40R^2=0.40 when driven by PBM-simulated values, increasing to R2=0.76R^2=0.76 after excluding a single outlier strategy. Fourth, high computational efficiency was achieved by the Unity rendering engine, with a rendering time below 10 ms per frame at a low resolution. Fifth, it was demonstrated that a lighting-control policy can be learned and then operated by observing crop images without biomass estimation, providing the a proof of concept of vision-based reinforcement learning in CEA. Collectively, these results establish LettuceVisSim as a viable simulator for vision-based RL research in CEA. Declaration of competing interest The financial support of this paper was provided by the China Scholarship Council. All authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. CRediT authorship contribution statement Ziye Zhu: Conceptualisation, Data curation, Formal analysis, Investigation, Methodology, Software, Validation, Visualisation, Writing – original draft, Writing – review and editing. Bert van ’t Ooster: Conceptualisation, Methodology, Writing – review and editing. Congcong Sun: Methodology, Supervision, Writing – review and editing. Eldert van Henten: Conceptualisation, Supervision, Writing – review and editing. Sjoerd Boersma: Supervision, Writing – review and editing. Acknowledgements This work was supported by the China Scholarship Council (grant No. 202209110010). The authors thank the members of the Agricultural Biosystems Engineering (ABE) group at Wageningen University & Research for their valuable discussions and constructive feedback throughout this work. Declaration of generative AI and AI-assisted technologies in the manuscript preparation process During the preparation of this work the author(s) used ChatGPT in order to check for grammatical errors. After using this tool/service, the author(s) reviewed and edited the content as needed and take(s) full responsibility for the content of the published article. Data availability The datasets analysed in this study are publicly available from the 3rd Autonomous Greenhouse Challenge [Hemming et al., 2021, Petropoulou et al., 2023]. A demonstration implementation of LettuceVisSim, including example configurations and scripts to run the simulator, is available at https://github.com/ThomasZiyeZhu/LettuceVisSim.git. Appendix A Process-based model equations This appendix summarises the process-based model (PBM) equations used in this study. Let p denote the set of model parameters appearing in the PBM formulation. The governing equations are given below, and Table 1 lists the definitions, values, and units of the individual parameters in p. X˙n X_n =cafphot−rgrXs−fresp−1−cbcbrgrXs, =c_af_phot-r_grX_s-f_resp- 1-c_bc_br_grX_s, (17) X˙s X_s =rgrXs, =r_grX_s, (18) where rgr r_gr =cgr,maxXncgXs+XncQ10,gr(T−20)/10, =c_gr,max X_nc_gX_s+X_n\,c_Q10,gr^(T-20)/10, (19) fresp f_resp =[cresp,sht(1−ct)Xs+cresp,rtctXs]cQ10,resp(T−25)/10, = [c_resp,sht(1-c_t)X_s+c_resp,rtc_tX_s ]c_Q10,resp^(T-25)/10, (20) fphot f_phot =(1−exp[−cKclar(1−ct)Xs])fphot,max, = (1- \! [-c_Kc_lar(1-c_t)X_s ] )f_phot,max, (21) fphot,max f_phot,max =eIgCO2cw(CCO2−G)eI+gCO2cw(CCO2−G), = eIg_CO_2c_w(C_CO_2-G)eI+g_CO_2c_w(C_CO_2-G), (22) G G =cGcQ10,G(T−20)/10, =c_Gc_Q10,G^(T-20)/10, (23) e e =ceCCO2−GCCO2+2G, =c_e C_CO_2-GC_CO_2+2G, (24) gCO2−1 g_CO_2^-1 =gbnd−1+gstm−1+gcar−1, =g_bnd^-1+g_stm^-1+g_car^-1, (25) gcar g_car =−1.32×10−5T2+5.94×10−4T−2.64×10−3. =-1.32× 10^-5T^2+5.94× 10^-4T-2.64× 10^-3. (26) Table 1: Model parameters used in the process-based lettuce growth model. Parameter Definition Unit cac_a CO2 to CH2O conversion factor – cbc_b Yield factor – cgr,maxc_gr,max Saturation growth rate at 20∘C s-1 cgc_g Growth rate coefficient – cQ10,grc_Q10,gr Temperature sensitivity of growth – cresp,shtc_resp,sht Shoot maintenance respiration coefficient at 25∘C s-1 cresp,rtc_resp,rt Root maintenance respiration coefficient at 25∘C s-1 cQ10,respc_Q10,resp Temperature sensitivity of respiration – ctc_t Root-to-total dry mass ratio (hydroponic) – cKc_K Extinction coefficient – clarc_lar Structural leaf area ratio m2 g-1 cwc_w CO2 density g m-3 cGc_G CO2 compensation point at 20∘C mL L-1 cQ10,Gc_Q10,G Temperature sensitivity of CO2 compensation point – cec_e Quantum use efficiency g J-1 gbndg_bnd Boundary layer conductance m s-1 gstmg_stm Stomatal conductance m s-1 Appendix B DeepLabv3+ training and validation performance The performance of the segmentation model was quantified with the same mean intersection over union (mIoU) metric as used by Petropoulou et al. [2023], which is expressed as a percentage and is defined as mIoU=12(|MGT,lettuce∩Mlettuce||MGT,lettuce∪Mlettuce|+|MGT,background∩Mbackground||MGT,background∪Mbackground|)×100%mIoU= 12 ( |M_GT,lettuce∩ M_lettuce | |M_GT,lettuce∪ M_lettuce |+ |M_GT,background∩ M_background | |M_GT,background∪ M_background | )× 100\% (27) in which M denotes the mask of the lettuce class and of the background class, respectively, and |⋅||·| denotes the number of pixels in a mask. The mIoU of 93.5% reported in Section 2.2.2 was obtained on the held-out test set. The training and validation loss curves and the validation mIoU over the training epochs are shown in Fig. 1. Figure 1: Training performance of DeepLabv3+. Left: training and validation loss over the training epochs. Right: validation mean intersection over union (mIoU) over the training epochs. Appendix C Plant density and annotated image-based lettuce counts The relation between the recorded plant density and the number of lettuce plants visible within the camera field of view, as derived from the annotated images, is shown in Fig. 1 Figure 1: Temporal changes in plant density pdpd and in the visible plant counts within the camera field of view, for each of the 12 cultivation strategies. Appendix D Evaluation metrics Throughout this study, predictive performance is quantified using the coefficient of determination (R2R^2) and the relative root mean squared error (RRMSE). Let oio_i denote the iith observed value, o^i o_i the corresponding predicted or simulated value, o¯ o the mean of all observed values, and n the total number of observations. The metrics are defined as R2=1−∑i=1n(oi−o^i)2∑i=1n(oi−o¯)2,R^2=1- _i=1^n(o_i- o_i)^2 _i=1^n(o_i- o)^2, (28) RMSE=1n∑i=1n(oi−o^i)2,RMSE= 1n _i=1^n(o_i- o_i)^2, (29) RRMSE=RMSEo¯×100%.RRMSE= RMSE o× 100\%. (30) The specific roles of oio_i and o^i o_i differ per experiment; the precise variable definitions are given in the description of each experiment in Section 2.3. Appendix E Vision-based reinforcement network architecture and training details This appendix details the network architecture and training configuration used in the vision-based RL demonstration. Network architecture. An asymmetric actor–critic architecture was used. The actor encodes the 84×8484× 84 RGB image observation with a convolutional network into a 256-dimensional feature vector and therefore depends on the image alone; a fully connected head then outputs a Gaussian over a normalised action in [0,1][0,1], rescaled to the physical range [0,360]μmolm−2s−1[0,360]~ \ m^-2\ s^-1. The critic uses the same image encoder but additionally concatenates the privileged true shoot dry weight (a scalar) during training, and outputs a scalar state-value estimate through a fully connected head. The implementation was based on Stable-Baselines3 [Raffin et al., 2021]. Training setup. The full set of PPO hyperparameters is listed in Table 1. Table 1: PPO training hyperparameters used in the vision-based RL demonstration. Hyperparameter Value Description Learning rate 3×10−43× 10^-4 Adam optimiser learning rate Discount factor 0.99 Future reward discount GAE parameter 0.95 Generalized advantage estimation Clip range 0.2 PPO surrogate objective clipping Entropy coefficient 0.0 Exploration bonus weight Value function coefficient 0.5 Critic loss scaling Gradient norm clipping 0.5 Maximum gradient norm Steps per environment 2048 Rollout length per environment Mini-batch size 64 Batch size for gradient updates Number of epochs 10 Passes over collected data per update Total timesteps 3×1053× 10^5 Training duration Appendix F Per-strategy evaluation metrics The per-strategy evaluation metrics that accompany Fig. 5, Fig. 8 and Fig. 9 are listed in Table 1, Table 2 and Table 3, respectively. Table 1: Per-strategy agreement between the shoot dry weight simulated by the process-based model and the measured shoot dry weight, for the 12 test trajectories shown in Fig. 5. Each trajectory was generated with the fold-specific parameters from the cross-validation run in which that strategy was held out. n is the number of destructive sampling occasions of that strategy. Strategy R2R^2 RMSE (g plant-1) RRMSE (%) n koala1 0.632 2.849 60.1 8 monday-lettuce1 0.991 0.400 9.8 8 digital-cucumbers1 0.728 1.130 53.6 7 cva1 0.985 0.616 13.7 8 veggie-might1 −-1.026 4.381 144.0 8 reference1 0.970 0.629 17.6 7 digital-cucumbers2 0.860 2.223 33.6 8 koala2 0.953 1.400 22.4 8 monday-lettuce2 0.746 2.141 43.6 8 cva2 0.952 1.328 21.4 8 veggie-might2 0.957 1.422 19.6 8 reference2 0.858 1.737 36.0 7 Table 2: Per-strategy agreement between the ground coverage ratio simulated with measured shoot dry weight and the daily averaged image-derived ground coverage ratio, for the 12 cultivation strategies shown in Fig. 8. n is the number of measurement days of that strategy. Strategy R2R^2 RMSE RRMSE (%) n koala1 0.89 0.088 12.2 8 monday-lettuce1 0.99 0.032 4.2 8 digital-cucumbers1 0.88 0.095 14.9 7 cva1 0.95 0.065 9.2 8 veggie-might1 −-0.25 0.201 36.3 8 reference1 0.93 0.076 12.2 6 digital-cucumbers2 0.91 0.079 10.0 8 koala2 0.96 0.061 7.5 8 monday-lettuce2 0.91 0.090 11.5 7 cva2 0.98 0.052 7.0 7 veggie-might2 0.98 0.043 5.8 7 reference2 0.94 0.063 9.2 6 Table 3: Per-strategy agreement between the ground coverage ratio simulated with the shoot dry weight of the process-based model and the image-derived ground coverage ratio, for the 12 cultivation strategies shown in Fig. 9. Each strategy was driven by the fold-specific parameters from the cross-validation run in which it was held out. n is the number of individual images of that strategy. Strategy R2R^2 RMSE RRMSE (%) n koala1 0.38 0.170 23.0 412 monday-lettuce1 0.95 0.057 7.3 428 digital-cucumbers1 0.74 0.137 19.6 360 cva1 0.93 0.064 8.8 440 veggie-might1 −-3.56 0.292 49.5 469 reference1 0.85 0.103 14.4 403 digital-cucumbers2 0.91 0.060 7.1 421 koala2 0.55 0.149 17.3 443 monday-lettuce2 0.54 0.153 17.8 403 cva2 0.91 0.078 9.5 393 veggie-might2 0.91 0.067 8.4 400 reference2 0.64 0.135 18.5 353 References An et al. (2021) Z. An, X. Cao, Y. Yao, W. Zhang, L. Li, Y. Wang, S. Guo, and D. Luo A Simulator-based Planning Framework for Optimizing Autonomous Greenhouse Control Strategy. Proceedings of the International Conference on Automated Planning and Scheduling 31, p. 436–444 (en). External Links: ISSN 2334-0843, Link, Document Cited by: §1. Baek et al. (2025) M. H. Baek, I. S. Kim, and J. S. Jo Non-destructive estimation of leaf area, fresh weight, and dry weight in leafy vegetables using image analysis. Journal of Bio-Environment Control 34 (4), p. 485–495 (en). External Links: ISSN 1229-4675, 2765-3641, Link, Document Cited by: §2.1.2. J. C. Bakker, G. P. A. Bot, H. Challa, and N. J. Van de Braak (Eds.) (1995) J. C. Bakker, G. P. A. Bot, H. Challa, and N. J. Van de Braak (Eds.) Greenhouse climate control: an integrated approach. Wageningen Academic Publishers, Netherlands (English). External Links: ISBN 9789074134170, Document Cited by: §1. Bates et al. (2024) S. Bates, T. Hastie, and R. Tibshirani Cross-validation: what does it estimate and how well does it do it?. Journal of the American Statistical Association 119 (546), p. 1434–1445. External Links: ISSN 0162-1459, Link, Document Cited by: §2.3.1. Boersma et al. (2022) S. Boersma, S. Van Mourik, B. Xin, G. Kootstra, and D. Bustos-Korts Nonlinear Observability Analysis and Joint State and Parameter Estimation in a Lettuce Greenhouse using Ensemble Kalman Filtering. IFAC-PapersOnLine 55 (32), p. 141–146 (en). External Links: ISSN 24058963, Link, Document Cited by: §2.1. Buck-Sorlin (2013) G. Buck-Sorlin Functional-Structural Plant Modeling. In Encyclopedia of Systems Biology, W. Dubitzky, O. Wolkenhauer, K. Cho, and H. Yokota (Eds.), p. 778–781 (en). External Links: ISBN 978-1-4419-9863-7, Link, Document Cited by: §1. Bumgarner et al. (2012) N. R. Bumgarner, W. S. Miller, and M. D. Kleinhenz Digital Image Analysis to Supplement Direct Measures of Lettuce Biomass. HortTechnology 22 (4), p. 547–555 (en). External Links: ISSN 1063-0198, 1943-7714, Link, Document Cited by: §1. Chen et al. (2018) L. Chen, Y. Zhu, G. Papandreou, F. Schroff, and H. Adam Encoder-decoder with atrous separable convolution for semantic image segmentation. In Computer Vision – ECCV 2018, V. Ferrari, M. Hebert, C. Sminchisescu, and Y. Weiss (Eds.), Lecture Notes in Computer Science, Vol. 11211, p. 833–851. External Links: Document Cited by: §2.2.2. Chen et al. (2025) S. Chen, A. Liu, F. Tang, P. Hou, Y. Lu, and P. Yuan A Review of Environmental Control Strategies and Models for Modern Agricultural Greenhouses. Sensors (Basel, Switzerland) 25 (5), p. 1388. External Links: ISSN 1424-8220, Link, Document Cited by: §1. Concepcion Ii et al. (2020) R. S. Concepcion Ii, J. D. Alejandrino, S. C. Lauguico, R. R. Tobias, E. Sybingco, E. P. Dadios, and A. A. Bandala Lettuce growth stage identification based on phytomorphological variations using coupled color superpixels and multifold watershed transformation. International Journal of Advances in Intelligent Informatics 6 (3), p. 261 (en). External Links: ISSN 2548-3161, 2442-6571, Link, Document Cited by: §1. Croitoru et al. (2023) F. Croitoru, V. Hondru, R. T. Ionescu, and M. Shah Diffusion Models in Vision: A Survey. IEEE Transactions on Pattern Analysis and Machine Intelligence 45 (9), p. 10850–10869. External Links: ISSN 1939-3539, Link, Document Cited by: §1. Di Paola et al. (2016) A. Di Paola, R. Valentini, and M. Santini An overview of available crop growth and yield models for studies and assessments in agriculture. Journal of the Science of Food and Agriculture 96 (3), p. 709–714 (en). Note: _eprint: https://onlinelibrary.wiley.com/doi/pdf/10.1002/jsfa.7359 External Links: ISSN 1097-0010, Link, Document Cited by: §1. Droutsas et al. (2022) I. Droutsas, A. J. Challinor, C. R. Deva, and E. Wang Integration of machine learning into process-based modelling to improve simulation of complex crop responses. in silico Plants 4 (2), p. diac017. External Links: ISSN 2517-5025, Link, Document Cited by: §2.3.1. Du et al. (2021) J. Du, J. Fan, C. Wang, X. Lu, Y. Zhang, W. Wen, S. Liao, X. Yang, X. Guo, and C. Zhao Greenhouse-based vegetable high-throughput phenotyping platform and trait evaluation for large-scale lettuces. Computers and Electronics in Agriculture 186, p. 106193 (en). External Links: ISSN 01681699, Link, Document Cited by: §1. Gautron et al. (2022) R. Gautron, O. Maillard, P. Preux, M. Corbeels, and R. Sabbadin Reinforcement learning for crop management support: review, prospects and challenges. Computers and Electronics in Agriculture 200, p. 107182 (en). External Links: ISSN 0168-1699, Link, Document Cited by: §1. Geldhof et al. (2021) B. Geldhof, J. Pattyn, D. Eyland, S. Carpentier, and B. Van de Poel A digital sensor to measure real-time leaf movements and detect abiotic stress in plants. Plant Physiology 187 (3), p. 1131–1148. External Links: ISSN 0032-0889, Link, Document Cited by: §4.2. Guo and Shen (2016) Y. Guo and Y. Shen Agricultural water supply/demand changes under projected future climate change in the arid region of northwestern China. Journal of Hydrology 540, p. 257–273 (en). External Links: ISSN 0022-1694, Link, Document Cited by: §1. S. D. Gupta and Y. Ibaraki (Eds.) (2014) S. D. Gupta and Y. Ibaraki (Eds.) Plant Image Analysis: Fundamentals and Applications. 1st edition, CRC Press, Boca Raton (en). External Links: Document, ISBN 9780429072345 Cited by: §1. Hemming et al. (2021) S. Hemming, F. De Zwart, A. Elings, M. Bijlaard, B. Van Marrewijk, and A. S. Petropoulou [Dataset] 3rd Autonomous Greenhouse Challenge: Online Challenge Lettuce Images. 4TU.ResearchData. External Links: Link, Document Cited by: §2.2.1, Data availability. Hossain et al. (2020) A. Hossain, T. J. Krupnik, J. Timsina, M. G. Mahboob, A. K. Chaki, M. Farooq, R. Bhatt, S. Fahad, and M. Hasanuzzaman Agricultural Land Degradation: Processes and Problems Undermining Future Food Security. In Environment, Climate, Plant and Vegetation Growth, S. Fahad, M. Hasanuzzaman, M. Alam, H. Ullah, M. Saeed, I. Ali Khan, and M. Adnan (Eds.), p. 17–61 (en). External Links: ISBN 978-3-030-49732-3, Link, Document Cited by: §1. Hu and You (2022) G. Hu and F. You Renewable energy-powered semi-closed greenhouse for sustainable crop production using model predictive control and machine learning for energy management. Renewable and Sustainable Energy Reviews 168, p. 112790. External Links: ISSN 1364-0321, Link, Document Cited by: §1. Hussain et al. (2026) K. Hussain, T. Hilger, E. E. Hakki, A. Ilyas, S. Gezgin, and C. Wongleecharoen Simulation of resources use and abiotic stress management in various maize-based cropping systems. Frontiers in Plant Science 16, p. 1743567. External Links: ISSN 1664-462X, Link, Document Cited by: §2.3.1. Kalashnikov et al. (2018) D. Kalashnikov, A. Irpan, P. Pastor, J. Ibarz, A. Herzog, E. Jang, D. Quillen, E. Holly, M. Kalakrishnan, V. Vanhoucke, and S. Levine Scalable deep reinforcement learning for vision-based robotic manipulation. In Proceedings of the 2nd Conference on Robot Learning, A. Billard, A. Dragan, J. Peters, and J. Morimoto (Eds.), Proceedings of Machine Learning Research, Vol. 87, p. 651–673. External Links: Link Cited by: §1. Kim and Van Iersel (2022) C. Kim and M. W. Van Iersel Morphological and Physiological Screening to Predict Lettuce Biomass Production in Controlled Environment Agriculture. Remote Sensing 14 (2), p. 316 (en). External Links: ISSN 2072-4292, Link, Document Cited by: §4.2. Kirillov et al. (2023) A. Kirillov, E. Mintun, N. Ravi, H. Mao, C. Rolland, L. Gustafson, T. Xiao, S. Whitehead, A. C. Berg, W. Lo, P. Dollár, and R. Girshick Segment Anything. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), p. 4015–4026. External Links: Document Cited by: §2.2.2. Kozai et al. (2019) T. Kozai, G. Niu, and M. Takagaki Plant Factory: An Indoor Vertical Farming System for Efficient Quality Food Production. Academic Press (en). External Links: ISBN 978-0-12-816692-5 Cited by: §1. Li et al. (2022) Q. Li, H. Gao, X. Zhang, J. Ni, and H. Mao Describing lettuce growth using morphological features combined with nonlinear models. Agronomy 12 (4), p. 860 (en). External Links: ISSN 2073-4395, Link, Document Cited by: §2.1.2. Li et al. (2024) Y. Li, J. Du, and W. Jiang Reinforcement learning for process control with application in semiconductor manufacturing. IISE Transactions 56 (6), p. 585–599. External Links: Document Cited by: §1. Liu and Van Iersel (2022) J. Liu and M. W. Van Iersel Far-red light effects on lettuce growth and morphology in indoor production are cultivar specific. Plants 11 (20), p. 2714. External Links: ISSN 2223-7747, Link, Document Cited by: §4.2. Louarn and Song (2020) G. Louarn and Y. Song Two decades of functional–structural plant modelling: now addressing fundamental questions in systems biology and predictive ecology. Annals of Botany 126 (4), p. 501–509. External Links: ISSN 0305-7364, Link, Document Cited by: §1. Mallick et al. (2025) S. Mallick, F. Airaldi, A. Dabiri, C. Sun, and B. De Schutter Reinforcement Learning-based Model Predictive Control for Greenhouse Climate Control. Smart Agricultural Technology 10, p. 100751 (en). Note: arXiv:2409.12789 [eess] External Links: ISSN 2772-3755, Link, Document Cited by: §1. Mnih et al. (2015) V. Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski, S. Petersen, C. Beattie, A. Sadik, I. Antonoglou, H. King, D. Kumaran, D. Wierstra, S. Legg, and D. Hassabis Human-level control through deep reinforcement learning. Nature 518 (7540), p. 529–533. External Links: Document Cited by: §1. Morcego et al. (2023) B. Morcego, W. Yin, S. Boersma, E. J. Van Henten, V. Puig, and C. Sun Reinforcement Learning versus Model Predictive Control on greenhouse climate control. Computers and Electronics in Agriculture 215, p. 108372. External Links: ISSN 0168-1699, Link, Document Cited by: §1. Parr et al. (2021) C. Parr, D. Lemay, C. Owen, M. J. Woodward-Greene, and J. Sun Multimodal AI to Improve Agriculture. IT Professional 23, p. 53–57. External Links: Document Cited by: §1. Petropoulou et al. (2023) A. S. Petropoulou, B. Van Marrewijk, F. De Zwart, A. Elings, M. Bijlaard, T. Van Daalen, G. Jansen, and S. Hemming Lettuce Production in Intelligent Greenhouses—3D Imaging and Computer Vision for Plant Spacing Decisions. Sensors 23 (6), p. 2929 (en). Note: Number: 6 External Links: ISSN 1424-8220, Link, Document Cited by: Appendix B, §2.2.1, §2.2.2, §2.2.2, Data availability. Raffin et al. (2021) A. Raffin, A. Hill, A. Gleave, A. Kanervisto, M. Ernestus, and N. Dormann Stable-Baselines3: Reliable Reinforcement Learning Implementations. Journal of Machine Learning Research 22 (268), p. 1–8. External Links: Link Cited by: Appendix E. Roberts et al. (2017) D. R. Roberts, V. Bahn, S. Ciuti, M. S. Boyce, J. Elith, G. Guillera-Arroita, S. Hauenstein, J. J. Lahoz-Monfort, B. Schröder, W. Thuiller, D. I. Warton, B. A. Wintle, F. Hartig, and C. F. Dormann Cross-validation strategies for data with temporal, spatial, hierarchical, or phylogenetic structure. Ecography 40 (8), p. 913–929. External Links: ISSN 0906-7590, Link, Document Cited by: §2.3.1. Schulman et al. (2017) J. Schulman, F. Wolski, P. Dhariwal, A. Radford, and O. Klimov Proximal Policy Optimization Algorithms. arXiv preprint arXiv:1707.06347. External Links: Link, Document Cited by: §2.3.5. Song et al. (2021) Y. Song, S. Naji, E. Kaufmann, A. Loquercio, and D. Scaramuzza Flightmare: a flexible quadrotor simulator. In Proceedings of the 2020 Conference on Robot Learning, J. Kober, F. Ramos, and C. Tomlin (Eds.), Proceedings of Machine Learning Research, Vol. 155, p. 1147–1157. External Links: Link Cited by: §1, §1. Sun et al. (2025) W. Sun, A. Coules, C. Zhao, and C. Lu A lettuce growth model responding to a broad range of greenhouse climates. Biosystems Engineering 250, p. 285–305. External Links: ISSN 1537-5110, Document, Link Cited by: §4.1. Sutton and Barto (2018) R. S. Sutton and A. G. Barto Reinforcement Learning: An Introduction. 2nd edition, The MIT Press. External Links: Link Cited by: §1. Svensen et al. (2024) J. L. Svensen, X. Cheng, S. Boersma, and C. Sun Chance-constrained stochastic MPC of greenhouse production systems with parametric uncertainty. Computers and Electronics in Agriculture 217, p. 108578 (en). External Links: ISSN 01681699, Link, Document Cited by: §2.1. Tan et al. (2025) D. Tan, M. Beck, C. P. Bidinosti, R. H. Gulden, and C. J. Henry Generative diffusion models for agricultural AI: plant image generation, indoor-to-outdoor translation, and expert preference alignment. arXiv. Note: arXiv:2512.19632 [cs] External Links: Link, Document Cited by: §1. Van Henten and Van Straten (1994) E. J. Van Henten and G. Van Straten Sensitivity Analysis of a Dynamic Growth Model of Lettuce. Journal of Agricultural Engineering Research 59 (1), p. 19–31. External Links: ISSN 0021-8634, Link, Document Cited by: §2.3.1. Van Henten (1994a) E. J. Van Henten Greenhouse climate management: an optimal control approach. Ph.D. Thesis, Landbouwuniversiteit Wageningen, Netherlands, (English). Note: WU thesis 1878 External Links: ISBN 9789054853213, Document Cited by: §1, §1. Van Henten (1994b) E. J. Van Henten Validation of a dynamic lettuce growth model for greenhouse climate control. Agricultural Systems 45 (1), p. 55–72 (en). External Links: ISSN 0308521X, Link, Document Cited by: §1, §2.1.1. Van Laatum et al. (2025) B. Van Laatum, E. J. Van Henten, and S. Boersma GreenLight-Gym: reinforcement learning benchmark environment for control of greenhouse production systems. IFAC-PapersOnLine 59 (23), p. 437–442. External Links: Document Cited by: §1, §4.4. Xu et al. (2021) D. Xu, H. A. Ahmed, Y. Tong, Q. Yang, and L. G. Van Willigenburg Optimal control as a tool to investigate the profitability of a Chinese plant factory - lettuce production system. Biosystems Engineering 208, p. 319–332 (en). External Links: ISSN 15375110, Link, Document Cited by: §1. Xu et al. (2018) D. Xu, S. Du, and L. G. Van Willigenburg Adaptive two time-scale receding horizon optimal control for greenhouse lettuce cultivation. Computers and Electronics in Agriculture 146, p. 93–103. External Links: ISSN 0168-1699, Link, Document Cited by: §1. Xu et al. (2025) D. Xu, L. Xu, S. Wang, M. Wang, J. Ma, and C. Shi Rule-based year-round model predictive control of greenhouse tomato cultivation: A simulation study. Information Processing in Agriculture 12 (3), p. 344–357. External Links: ISSN 2214-3173, Link, Document Cited by: §1. Xu et al. (2020) D. Xu, Q. Yang, Y. Tong, and L. G. Van Willigenburg Optimal control of LED light intensity in a plant factory. In 2020 39th Chinese Control Conference (C), Shenyang, China, p. 1362–1367 (en). External Links: ISBN 978-988-15639-0-3, Link, Document Cited by: §2.1. Zangana et al. (2025) H. M. Zangana, S. Li, and S. Wani Diffusion models for agricultural imaging: a systematic review of methods, applications and future prospects. IMPACT in Agriculture 1 (1), p. 1–11 (en). External Links: Link, Document Cited by: §1. Zhao et al. (2020) W. Zhao, J. P. Queralta, and T. Westerlund Sim-to-real transfer in deep reinforcement learning for robotics: a survey. In 2020 IEEE Symposium Series on Computational Intelligence (SSCI), p. 737–744 (en). External Links: Link, Document Cited by: §1.