Informed Learning for Estimating Drought Stress at Fine-Scale Resolution Enables Accurate Yield Prediction

TL;DR

This work addresses the challenge of predicting crop yield under drought stress by combining physics-based crop knowledge with data-driven learning. It introduces a physics-informed neural network that jointly learns the actual evapotranspiration $ET_a$ and the yield sensitivity to water scarcity $K_y$ from pixel-level multispectral and weather data, using simulated maximum ET $ET_x$ to enforce a physically consistent yield relation. The approach yields state-of-the-art predictive performance (up to $R^2 \approx 0.82$) while providing interpretable drought stress fields at fine spatial resolution, and it quantifies uncertainty via deep ensembles. The method has practical implications for farmers, policymakers, and industry aiming to improve resilience of agriculture under climate variability.

Abstract

Water is essential for agricultural productivity. Assessing water shortages and reduced yield potential is a critical factor in decision-making for ensuring agricultural productivity and food security. Crop simulation models, which align with physical processes, offer intrinsic explainability but often perform poorly. Conversely, machine learning models for crop yield modeling are powerful and scalable, yet they commonly operate as black boxes and lack adherence to the physical principles of crop growth. This study bridges this gap by coupling the advantages of both worlds. We postulate that the crop yield is inherently defined by the water availability. Therefore, we formulate crop yield as a function of temporal water scarcity and predict both the crop drought stress and the sensitivity to water scarcity at fine-scale resolution. Sequentially modeling the crop yield response to water enables accurate yield prediction. To enforce physical consistency, a novel physics-informed loss function is proposed. We leverage multispectral satellite imagery, meteorological data, and fine-scale yield data. Further, to account for the uncertainty within the model, we build upon a deep ensemble approach. Our method surpasses state-of-the-art models like LSTM and Transformers in crop yield prediction with a coefficient of determination ($R^2$-score) of up to 0.82 while offering high explainability. This method offers decision support for industry, policymakers, and farmers in building a more resilient agriculture in times of changing climate conditions.

Figures (5)

• Figure 1: Overview of the physics-guided method for crop yield prediction. The training (left) and the inference (right) are displayed. Highlight: The Data is modeled pixel-wise by optimizing the model to approximate crop yield using the yield response to water function, which enhances the estimation of actual evapotranspiration, an indicator of drought stress. Both components are estimated at fine-scale resolution. In contrast, the simulated maximum evapotranspiration lacks spatial detail.
• Figure 2: Example time series from seeding to harvesting of the training and simulation data of a randomly selected field. Top: Time series of satellite images in RGB. Center: Time Series of meteorological data. Bottom: Simulated maximum and actual evapotranspiration (ET). Takeaway: Maximum and actual ET values are almost consistently identical throughout the season in this example.
• Figure 3: Example predictions of an entire field. Each row represents a single field. Left: Ground truth yield map, center: predicted yield map, right: predicted actual ET. Highlight: The actual ET originally had no spatial resolution at the pixel level. Now we observe a clear correlation between the actual ET and the predicted yield, such that high ET values correlate with high yield values.
• Figure 4: Single field example of the predicted agronomic properties. Left: Temporal visualization of the simulated maximum $ET_x$ and learned actual $ET_a$. Right: Temporal visualization of the estimated susceptibility to water scarcity ($K_y$) and the NDVI. Predictions are illustrated with $\pm2\sigma$ to account for uncertainty. Highlight: Learned actual $ET_a$ and $K_y$ values follow key physical principles.
• Figure 5: Visualization of agronomic properties of the entire dataset. Left: Temporal illustration of the simulated maximum ($ET_x^{sim}$) and learned actual ($ET_a^{pred}$) crop evapotranspiration (ET), an indicator of drought stress. Right: The reduction in $ET_a$ compared to $ET_x$ is used to derive the reduction in yield (yield loss) using the yield response to water function doorenbos1979yield. The model accuracy is expressed by the $R^2$-score over time. Predictions are illustrated with $\pm2\sigma$ using a deep ensemble approach. Highlight: The estimated yield loss correlates with the learned drought stress while outperforming state-of-the-art models.