Physics-Informed Neural Networks for Predicting Nitrous Oxide Flux

Nitrous oxide (N2O) is a potent greenhouse gas primarily emitted from agricultural soils. Predicting these emissions is notoriously difficult due to their episodic nature and sensitivity to complex environmental variables. While process-based models (like DayCent and Cycles) and machine learning models are commonly used, both struggle with accuracy and site-specific calibration. This paper investigates whether Physics-Informed Neural Networks (PINNs)—which integrate mechanistic biogeochemical equations into the neural network loss function—can improve predictive performance and generalization compared to traditional approaches.

The authors constructed a PINN using a Multi-Layer Perceptron (MLP) architecture. They derived a 'physics residual' based on the mechanistic equations of the DayCent model, which governs soil nitrogen biogeochemistry. The model was trained on a dataset of 8,271 daily observations across four geographically distinct US agricultural sites. To ensure consistent input data, the authors used Cycles-simulated variables for all features, avoiding the noise and gaps inherent in mixed-source observational data. The model was evaluated using both standard holdout validation and a more rigorous leave-one-site-out validation to test geographic generalizability.

The PINN significantly outperformed uncalibrated Cycles simulations across all tested configurations. While the baseline MLP (without physics constraints) achieved an R-squared of 0.411, the inclusion of physics constraints (the PINN approach) resulted in a notable trade-off: it degraded performance on in-distribution holdout data but consistently improved performance and reduced variability in leave-one-site-out validation. This suggests that the physics-informed loss acts as a regularizer, anchoring the model to biogeochemically plausible behaviors when it encounters unfamiliar soil conditions. However, the authors note that cross-site generalization remains a significant challenge, as the model failed to achieve positive R-squared values on the most geographically distinct held-out site.