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Exploring Physics-Informed Neural Networks for Crop Yield Loss Forecasting

Miro Miranda, Marcela Charfuelan, Andreas Dengel

TL;DR

The study tackles the gap between explainable physics-based crop models and scalable data-driven predictors by introducing a physics-informed recurrent neural network (PI-RNN) that estimates $ET_a$ and $K_y$ at pixel resolution. It constrains the learned dynamics with the crop-water-yield relation $Y_l = K_y (1 - ET_a/ET_x)$ and a two-term loss that enforces both predictive accuracy and physical plausibility, leveraging FAO-56 simulations for $ET_x$ and Sentinel-2 time series with climate data. Evaluated on 54k cereal yield samples from Switzerland (20172021) with 10-fold cross-validation, the PI-RNN achieves up to $R^2 = 0.77$, competitive with state-of-the-art transformers and surpassing a standard RNN, while providing interpretable intermediate outputs $ET_a$ and $K_y$. The approach highlights the practical potential of physics-informed outputs for high-resolution yield loss forecasting under extreme weather, enabling better adaptation strategies for policymakers, industry, and farmers.

Abstract

In response to climate change, assessing crop productivity under extreme weather conditions is essential to enhance food security. Crop simulation models, which align with physical processes, offer explainability but often perform poorly. Conversely, machine learning (ML) models for crop modeling are powerful and scalable yet operate as black boxes and lack adherence to crop growths physical principles. To bridge this gap, we propose a novel method that combines the strengths of both approaches by estimating the water use and the crop sensitivity to water scarcity at the pixel level. This approach enables yield loss estimation grounded in physical principles by sequentially solving the equation for crop yield response to water scarcity, using an enhanced loss function. Leveraging Sentinel-2 satellite imagery, climate data, simulated water use data, and pixel-level yield data, our model demonstrates high accuracy, achieving an R2 of up to 0.77, matching or surpassing state-of-the-art models like RNNs and Transformers. Additionally, it provides interpretable and physical consistent outputs, supporting industry, policymakers, and farmers in adapting to extreme weather conditions.

Exploring Physics-Informed Neural Networks for Crop Yield Loss Forecasting

TL;DR

The study tackles the gap between explainable physics-based crop models and scalable data-driven predictors by introducing a physics-informed recurrent neural network (PI-RNN) that estimates and at pixel resolution. It constrains the learned dynamics with the crop-water-yield relation and a two-term loss that enforces both predictive accuracy and physical plausibility, leveraging FAO-56 simulations for and Sentinel-2 time series with climate data. Evaluated on 54k cereal yield samples from Switzerland (20172021) with 10-fold cross-validation, the PI-RNN achieves up to , competitive with state-of-the-art transformers and surpassing a standard RNN, while providing interpretable intermediate outputs and . The approach highlights the practical potential of physics-informed outputs for high-resolution yield loss forecasting under extreme weather, enabling better adaptation strategies for policymakers, industry, and farmers.

Abstract

In response to climate change, assessing crop productivity under extreme weather conditions is essential to enhance food security. Crop simulation models, which align with physical processes, offer explainability but often perform poorly. Conversely, machine learning (ML) models for crop modeling are powerful and scalable yet operate as black boxes and lack adherence to crop growths physical principles. To bridge this gap, we propose a novel method that combines the strengths of both approaches by estimating the water use and the crop sensitivity to water scarcity at the pixel level. This approach enables yield loss estimation grounded in physical principles by sequentially solving the equation for crop yield response to water scarcity, using an enhanced loss function. Leveraging Sentinel-2 satellite imagery, climate data, simulated water use data, and pixel-level yield data, our model demonstrates high accuracy, achieving an R2 of up to 0.77, matching or surpassing state-of-the-art models like RNNs and Transformers. Additionally, it provides interpretable and physical consistent outputs, supporting industry, policymakers, and farmers in adapting to extreme weather conditions.
Paper Structure (4 sections, 5 equations, 2 figures, 2 tables)

This paper contains 4 sections, 5 equations, 2 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Results
  4. Conclusion

Figures (2)

  • Figure 1: (a) Framework for physics-informed yield loss forecasting. Data modalities, including Sentinel-2 imagery and climate variables, are used to train an RNN that predicts biophysical properties for each time point (actual water use ($ET_a$), and the crop susceptibility to water scarcity ($K_y$)). A simulation model predicts the maximum water use ($ET_x$). The predicted biophysical properties are used to calculate the actual yield loss ($Y_l$). We leverage prior knowledge describing the relationship between water use and the relative yield loss. (b) Performance plots for visual inspection of a single field. Yield data from cereals in Switzerland is shown, harvested in 2020.
  • Figure 2: Visualization of sequential estimations and predictions of biophysical crop properties and model performance up to 120 days before harvest.