# Deep Learning Meets Process-Based Models: A Hybrid Approach to Agricultural Challenges

arXiv: https://arxiv.org/abs/2504.16141 · HTML: https://mlsanity.com/paper/2504.16141/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 148 references that are in the map.
- First posted on arXiv 22 Apr 2025.

## Builds on (most cited first, 20 of 20)

- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equations](https://mlsanity.com/paper/2107.07871/) (2021)
- [A Differentiable Programming System to Bridge Machine Learning and Scientific Computing](https://mlsanity.com/paper/1907.07587/) (2019)
- [The physics of higher-order interactions in complex systems](https://mlsanity.com/paper/2110.06023/) (2021)
- [Physics-informed Convolutional Neural Networks for Temperature Field Prediction of Heat Source Layout without Labeled Data](https://mlsanity.com/paper/2109.12482/) (2021)
- [From calibration to parameter learning: Harnessing the scaling effects of big data in geoscientific modeling](https://mlsanity.com/paper/2007.15751/) (2020)
- [Physics-informed neural network simulation of multiphase poroelasticity using stress-split sequential training](https://mlsanity.com/paper/2110.03049/) (2021)
- [Optimizing Nitrogen Management with Deep Reinforcement Learning and Crop Simulations](https://mlsanity.com/paper/2204.10394/) (2022)
- [Coupling Machine Learning and Crop Modeling Improves Crop Yield Prediction in the US Corn Belt](https://mlsanity.com/paper/2008.04060/) (2020)
- [Simultaneous Corn and Soybean Yield Prediction from Remote Sensing Data Using Deep Transfer Learning](https://mlsanity.com/paper/2012.03129/) (2020)
- [A Latent Encoder Coupled Generative Adversarial Network (LE-GAN) for Efficient Hyperspectral Image Super-resolution](https://mlsanity.com/paper/2111.08685/) (2021)
- [Corn Yield Prediction with Ensemble CNN-DNN](https://mlsanity.com/paper/2105.14351/) (2021)
- [Estimating Crop Primary Productivity with Sentinel-2 and Landsat 8 using Machine Learning Methods Trained with Radiative Transfer Simulations](https://mlsanity.com/paper/2012.12101/) (2020)
- [BP-Triplet Net for Unsupervised Domain Adaptation: A Bayesian Perspective](https://mlsanity.com/paper/2202.09541/) (2022)
- [Learning safety in model-based Reinforcement Learning using MPC and Gaussian Processes](https://mlsanity.com/paper/2211.01860/) (2022)
- [Forward- or Reverse-Mode Automatic Differentiation: What's the Difference?](https://mlsanity.com/paper/2212.11088/) (2022)
- [ARTEMIS: Using GANs with Multiple Discriminators to Generate Art](https://mlsanity.com/paper/2311.08278/) (2023)
- [A Channel Attention-Driven Hybrid CNN Framework for Paddy Leaf Disease Detection](https://mlsanity.com/paper/2407.11753/) (2024)

## Built on by (most cited first, 1 of 1)

- [Uncertainty-aware neural emulation reveals climate-resilient maize traits at scale](https://mlsanity.com/paper/2605.22848/) (2026)

## Abstract (arXiv)

Process-based models (PBMs) and deep learning (DL) are two key approaches in agricultural modelling, each offering distinct advantages and limitations. PBMs provide mechanistic insights based on physical and biological principles, ensuring interpretability and scientific rigour. However, they often struggle with scalability, parameterisation, and adaptation to heterogeneous environments. In contrast, DL models excel at capturing complex, nonlinear patterns from large datasets but may suffer from limited interpretability, high computational demands, and overfitting in data-scarce scenarios. This study presents a systematic review of PBMs, DL models, and hybrid PBM-DL frameworks, highlighting their applications in agricultural and environmental modelling. We classify hybrid PBM-DL approaches into DL-informed PBMs, where neural networks refine process-based models, and PBM-informed DL, where physical constraints guide deep learning predictions. Additionally, we conduct a case study on crop dry biomass prediction, comparing hybrid models against standalone PBMs and DL models under varying data quality, sample sizes, and spatial conditions. The results demonstrate that hybrid models consistently outperform traditional PBMs and DL models, offering greater robustness to noisy data and improved generalisation across unseen locations. Finally, we discuss key challenges, including model interpretability, scalability, and data requirements, alongside actionable recommendations for advancing hybrid modelling in agriculture. By integrating domain knowledge with AI-driven approaches, this study contributes to the development of scalable, interpretable, and reproducible agricultural models that support data-driven decision-making for sustainable agriculture.