Organizations: Harvard University · Department of Biosystems Engineering and Soil Science University of Tennessee · Department of Mechanical and Aerospace Engineering University of Tennessee
Nitrous oxide (N2O) 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 N2O emissions occurring as a result of agricultural processes. Current approaches to predicting N2O 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 N2O 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 (R2=0.01), with our MLP baseline achieving mean R2=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 R2 across all seeds and λ values on our geographically distinct held-out site.
Accurate prediction of nitrous oxide (N2O) emissions from agriculture is important for assessing environmental impacts and supporting sustainable farming. However, prediction remains difficult because N2O emissions result from complex interactions among soil properties, climate, biochemical processes, and management practices, while high-quality observations are limited. Deep learning models can capture nonlinear relationships but often lack physical interpretability and may generalize poorly across environmental conditions. We propose the Knowledge-enhanced Agriculture-informed Neural Network (KAINN), a hybrid neural-mechanistic framework that extends the Agriculture-informed Neural Network by incorporating domain knowledge about fertilizer diffusion, soil respiration, and water-filled porosity. We evaluate KAINN using CNN, LSTM, and Transformer architectures across multiple growing seasons and input-feature configurations. The results show that KAINN generally provides lower root mean square error and mean absolute error and higher R-squared values than purely data-driven models and the original AINN. Analysis of the learned interfaces also shows smoother and more physically consistent parameter trajectories with reduced uncertainty. These findings demonstrate that incorporating environmental knowledge into neural networks can improve the reliability, interpretability, and generalization of agricultural N2O-emission predictions.
Time series forecasting has seen signicant advancements with the emergence of new deep learning models. However, forecasting time series in applications involving physical processes remains a major challenge. Despite the apparition of Physics Informed Neural Networks (PINN), recent models do not estimate unobservable intermediate physical variables, which are important for domain experts to understand the target behavior. To this end, we propose a Physics Informed Recurrent Neural Network (PIRNN) which predicts, along the target, unobservable variables on both historic data and forecast target. This approach enhances the model robustness and results interpretation using domain knowledge. Our method is easily adaptable to any physical model using several equations, each having its own set of unobservable variables, to describe it-self. As a case study, we incorporate physical equations used for groundwater levels predictions by the physical model called Gardenia. This model uses transfers equations between reservoirs, optimized with data assimilation, to simulate the evolution of groundwater levels. Evaluation includes several well known neural network models and the Gardenia model compared on twelve real world datasets. In addition, we study the impact of each component through an ablation study. Our model outperforms other models on ve out of the twelve datasets and our ablation study underlines the importance of having a physical background in our time series forecasting task. Finally, the coherence of the physical variables predicted by our neural network is assessed by a domain expert.
Etienne Lehembre, Pascal Audigane, Vincent Nguyen +2
Physics-Informed Neural Networks (PINNs) are an attractive tool for partial-observation problems in biology, where the governing dynamics are known but some compartments cannot be measured. Chemotherapy pharmacokinetics (PK) is a clean instance: drug concentration in plasma is routinely measured, but concentration in tissue -- which determines tumour kill and off-target toxicity -- is not. We benchmark a PINN against the standard clinical baseline (nonlinear least-squares on the analytical biexponential plasma solution, hereafter NLS) and a physics-agnostic neural baseline (a data-only MLP) on two PK problems. On the linear two-compartment problem, NLS is near-optimal; the PINN matches it to within a small constant factor while also producing the tissue curve in a single training pass, whereas the data-only MLP fails on tissue by roughly 10x. On a Michaelis-Menten extension (saturable elimination), the biexponential closed form no longer exists, so NLS is mis-specified and silently returns meaningless rate constants. The PINN instead exposes a deeper fact: the Michaelis-Menten two-compartment model is non-identifiable from plasma alone, and the PINN reports this honestly by converging to a basin with k12 -> 0. Adding two sparse tissue observations largely resolves identifiability: across five seeds the PINN recovers k21 to within 1% of truth and Vmax, Km to within one standard-deviation bar, while k12 moves in the correct direction (0.02 -> 0.82) but remains ~2 sigma below truth -- a recovery the closed-form NLS estimator cannot attempt at all, because its biexponential ansatz describes only plasma. Our claim is not that PINNs beat NLS. It is that PINNs offer a uniform recipe that ties the textbook estimator on the textbook problem, exposes structural identifiability that the textbook estimator hides, and absorbs heterogeneous measurements within a single loss.