Physics-Informed Neural Networks for Predicting Nitrous Oxide Flux

Nitrous oxide (N_2O) is the dominant ozone-depleting substance emitted in the 21st century, and the third largest contributor to anthropogenic greenhouse gases due to its high potency and long atmospheric lifetime, with more than 70% of N_2O emissions occurring as a result of agricultural processes. Current approaches to predicting N_2O flux emissions include process-based models such as DayCent and Cycles, as well as classical AI models, but the application of Physics-Informed Neural Networks (PINNs) to predicting N_2O flux emissions is largely underexplored. Our paper draws upon the mechanistic equations that underlie the DayCent family of process-based models to construct a rigorously derived, literature-traceable physics residual. We then build and train an MLP-based PINN on a multi-site agricultural dataset spanning four geographically distinct US agricultural sites. Across all tested values of the physics loss weighting hyperparameter λ, our PINN consistently and substantially outperformed uncalibrated Cycles simulation (R^2=0.01), with our MLP baseline achieving mean R^2=0.411 across ten random seeds. Physics constraints consistently degrade model performance in holdout validation, with marginal degradation at low λ and significant degradation at high λ, but consistently improve model performance and reduce performance variability in leave-one-site-out validation. This suggests that physics constraints sacrifice in-distribution accuracy for out-of-distribution robustness, anchoring the model toward biogeochemically plausible behavior on unfamiliar soil conditions --- though cross-site generalization remains challenging, with negative R^2 across all seeds and λ values on our geographically distinct held-out site.