From Data-Driven to Physics-Informed Surrogate Models for Reactive Nitrate Transport

Reactive nitrate transport in groundwater is governed by coupled advection–dispersion–reaction (ADR) dynamics and kinetically limited redox processes, including donor limitation and competition among electron acceptors. We compare two surrogate modeling approaches for reactive nitrate transport. The first is a physics-audited, data-driven approach based on a categorial boosting algorithm, with physical admissibility (e.g., non-negativity and ADR-consistent behavior) assessed via post-hoc diagnostics. The second is a physics-informed neural network (PINN) surrogate that embeds the ADR equation, boundary conditions, non-negativity, and a redox-ordering constraint directly into the training objective to promote mechanistic consistency. Both surrogates are trained and tested on the same one-dimensional PHREEQC benchmark suite spanning increasing hydrogeochemical complexity: linear denitrification, dual-linear nitrate–Fe(III) competition, dual-substrate Monod kinetics, and fully coupled dual-Monod redox systems. Predictive uncertainty is quantified to provide calibrated confidence bounds and identify regions of elevated sensitivity.

Results show that while both surrogates can interpolate reactive nitrate dynamics within the training domain, the PINN surrogate consistently provides superior physical consistency and robustness under increasing kinetic nonlinearity. Uncertainty estimates from the PINN are well calibrated, with prediction-interval widths increasing systematically near migrating reactive fronts where nonlinear redox competition amplifies model sensitivity. The results demonstrate that embedding governing physics directly into the learning process yields a more reliable and interpretable surrogate for uncertainty-aware reactive transport modeling, particularly in regimes dominated by nonlinear kinetics and competing redox pathways.