AgriPINN: A Process-Informed Neural Network for Interpretable and Scalable Crop Biomass Prediction Under Water Stress

TL;DR

AgriPINN introduces a process-informed neural network that embeds the LINTUL5 biomass-growth dynamics as a differentiable constraint within a CNN backbone to predict spatio-temporal crop AGB under water stress. The model unsupervisedly recovers latent physiological states (LAI, PAR, RUE, F_W) while achieving physiologically consistent biomass updates, leading to superior accuracy and robustness across large-scale spatial and temporal domains. Empirical results show up to 43% RMSE improvement over state-of-the-art data-driven baselines and strong spatial accuracy (R^2 ≈ 0.84) with 8x greater computational efficiency compared with traditional process-based simulations. The framework also demonstrates improved generalization under distribution shifts and enables latent-variable interpretability, offering a scalable, interpretable tool for irrigation planning, yield forecasting, and climate adaptation in agriculture.

Abstract

Accurate prediction of crop above-ground biomass (AGB) under water stress is critical for monitoring crop productivity, guiding irrigation, and supporting climate-resilient agriculture. Data-driven models scale well but often lack interpretability and degrade under distribution shift, whereas process-based crop models (e.g. DSSAT, APSIM, LINTUL5) require extensive calibration and are difficult to deploy over large spatial domains. To address these limitations, we propose AgriPINN, a process-informed neural network that integrates a biophysical crop-growth differential equation as a differentiable constraint within a deep learning backbone. This design encourages physiologically consistent biomass dynamics under water-stress conditions while preserving model scalability for spatially distributed AGB prediction. AgriPINN recovers latent physiological variables, including leaf area index (LAI), absorbed photosynthetically active radiation (PAR), radiation use efficiency (RUE), and water-stress factors, without requiring direct supervision. We pretrain AgriPINN on 60 years of historical data across 397 regions in Germany and fine-tune it on three years of field experiments under controlled water treatments. Results show that AgriPINN consistently outperforms state-of-the-art deep-learning baselines (ConvLSTM-ViT, SLTF, CNN-Transformer) and the process-based LINTUL5 model in terms of accuracy (RMSE reductions up to $43\%$) and computational efficiency. By combining the scalability of deep learning with the biophysical rigor of process-based modeling, AgriPINN provides a robust and interpretable framework for spatio-temporal AGB prediction, offering practical value for planning of irrigation infrastructure, yield forecasting, and climate-adaptation planning.

Figures (8)

• Figure 1: Workflow of the proposed AgriPINN model. The architecture integrates deep learning with process-based crop modeling by incorporating the LINTUL5 biomass-growth ODE as a soft constraint. The neural network predicts AGB together with latent physiological variables (LAI, RUE, PAR, $F_W$). These outputs are substituted into the biomass-growth equation to compute the process residual $r(\mathbf{p},t)$, where $\Delta AGB(\mathbf{p},t)$ is obtained as a time derivative using automatic differentiation. This residual defines the process-based loss, which is optimized jointly with the standard data loss to encourage biophysically consistent predictions across spatial locations and time steps.
• Figure 2: Comparison of (a) training time and (b) model size for AgriPINN and the baseline data-driven architectures. Training time (in minutes) is measured for a full pretraining run on a single NVIDIA RTX 2080 Ti GPU under identical batch size, optimizer, and learning-rate settings. Model size is reported as the number of trainable parameters (millions). AgriPINN requires substantially less training time and has a significantly smaller parameter count than the deeper transformer-based models, reflecting its computational efficiency despite achieving higher predictive accuracy.
• Figure 3: Temporal trajectories of winter wheat AGB under irrigated water treatment for four modelling approaches (AgriPINN, ConvLSTM–ViT, SLTF, and CNN–Transformer). Black dots indicate in-situ observations, orange lines show LINTUL5 simulations, and blue dashed lines denote model predictions. AgriPINN reproduces the observed AGB dynamics more accurately than the data-driven baselines and captures treatment-specific growth reductions, whereas baseline models fail to differentiate the water-stress scenarios. More detailed comparisons across different water treatments can be found in the Supplementary Materials.
• Figure 4: RMSPE (%) for AGB and latent physiological variables (LAI, PAR, RUE, $F_W$) under three water-stress treatments (sheltered, rainfed, irrigated). Error bars indicate standard deviations across all experimental plots. AgriPINN achieves consistently lower RMSPE and reduced variability across treatments compared with LINTUL5 and the data-driven baselines, demonstrating improved robustness in both biomass prediction and latent-variable reconstruction.
• Figure 5: Regression scatter plots between ground-truth AGB and AGB estimated from (a) LINTUL5, (b) the proposed AgriPINN, (c) ConvLSTM-ViT, (d) SLTF, and (e) CNN-Transformer. Ground-truth AGB is aggregated at the NUTS-3 regional scale (a total of 484 districts), while the estimated AGB values are statistically summarized at the same NUTS-3 level. The proposed model achieves the best predictive performance, with the highest $R^2$ (0.837) and the lowest RMSE (0.781), outperforming both the process-based model (second-best, $R^2 = 0.802$, RMSE $= 0.998$) and the data-driven models ($R^2 < 0.721$, RMSE $> 1.214$).