Nitrous oxide (N$_2$O) 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$_2$O emissions occurring as a result of agricultural processes. Current approaches to predicting N$_2$O 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$_2$O 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.
Accurate modeling of environmental systems is fundamental to scientific understanding and decision-making, yet remains challenging because observations are limited and physical dynamics vary across systems. Retrieval-augmented approaches offer a natural path to transfer knowledge across systems, but standard embedding-based retrieval does not guarantee consistency of underlying physical processes, since scenarios with similar embeddings may arise from different underlying mechanisms. We propose Physics-Informed Environmental Retrieval (PIER), a model-agnostic framework that augments embedding-based retrieval with a physics-aware stream that scores candidates by flux-response consistency with the target, using local verifiers trained on physics-derived flux features. A weight adjustment mechanism then learns per-scenario weights that adaptively balance the two retrieval streams based on diagnostic features summarizing physics-stream reliability. Experiments on 356 lakes across the Midwestern United States spanning 41 years show that PIER consistently outperforms baselines for water temperature and dissolved oxygen prediction, and serves as a general augmentation strategy across diverse backbones.
Ilektra Tsimpidi, George Georgoulas, Vidya Sumathy +1cs.LG
Soil Moisture (SM) modelling constitutes a complex spatiotemporal learning problem characterised by nonlinear environmental interactions, heterogeneous data sources, and limited ground observations. Physics-based approaches, such as water balance models, rely on explicit hydrological equations and high-quality inputs, but their computational cost and scalability limitations restrict large-scale deployment. Data-driven artificial intelligence (AI) methods have emerged as flexible alternatives, enabling the extraction of empirical relationships between soil moisture and environmental variables with reduced modelling assumptions. This work presents a structured survey of AI-based models for soil moisture estimation and classification. Existing approaches are organized into five categories: (a) statistical time-series models, (b) geostatistical methods (c) classical machine learning (ML) models, (d) Deep Learning (DL) models and (e) Probabilistic/Bayesian methods. These models leverage historical soil moisture records, meteorological variables, vegetation indices, topography, soil characteristics, and geolocation data to perform regression or classification tasks.