Organizations: Harvard University · Department of Biosystems Engineering and Soil Science University of Tennessee · Department of Mechanical and Aerospace Engineering University of Tennessee
Abstract
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.
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.
In this paper, we propose a Physics-Informed Neural Network framework for time-dependent simulations of pollution propagation originating from moving emission sources. We formulate a robust variational framework for the time-dependent advection-diffusion problem and establish the boundedness and inf-sup stability of the corresponding discrete weak formulation. Based on this mathematical foundation, we construct a robust loss function that is directly related to the true approximation error, defined as the difference between the neural network approximation and the (unknown) exact solution. Additionally, a collocation-based strategy is introduced to speed up neural network training. As a case study, we investigate pollution propagation caused by snowmobile traffic in Longyearbyen, Spitsbergen, supported by detailed in-field measurements collected using dedicated sensors. The proposed framework is applied to analyze the effects of thermal inversion on pollutant accumulation. Our results demonstrate that thermal inversion traps dense and humid air masses near the ground, significantly enhancing particulate matter (PM) concentration and worsening local air quality.
Leszek Siwik, Maciej Sikora, Natalia Leszczyńska +7
Modeling the Martian nightside thermosphere remains challenging due to sparse in situ sampling and strong coupling among transport, magnetic, and seasonal processes. Purely data-driven models can produce non-physical artifacts, such as density inversions, in poorly sampled altitude regimes. We present a multi-task physics-informed neural network that simultaneously predicts the base-10 logarithmic densities of four neutral species (O, CO2, N2, and Ar) using more than a decade of MAVEN/NGIMS observations (MY 32-38, 2014-2025). A shared backbone learns a common representation of the nightside thermospheric state and branches into species-specific output heads. A weak monotonicity prior is incorporated via automatic differentiation by penalizing positive vertical gradients in logarithmic density. Experiments using an orbit-disjoint train/validation/test split show that physics-informed regularization substantially reduces non-physical inversions while preserving predictive skill and slightly improving it in the best-performing configuration, as measured by RMSE, MAE, and R2. The resulting model provides a computationally efficient surrogate for nightside thermospheric reconstruction with improved vertical consistency.