Enhancing the interpretability of spatially variable N2O model predictions with soft sensors during wastewater treatment

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 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.

Vehicular traffic is a major source of air pollution; however, the contribution of remotely acquired traffic information to local machine-learning (ML) air-pollution models remains insufficiently characterised. This study evaluates four interpretable tree-based ML models (Random Forest, Extra Trees, LightGBM, and XGBoost) under six predictor scenarios combining progressively larger predictor sets, ranging from remotely acquired traffic, meteorological, and temporal variables alone to the inclusion of measurements from one and four neighbouring monitoring stations, to estimate NO$_2$, PM$_{10}$, PM$_{2.5}$, and O$_3$ concentrations across several sites in London. ML model performance was compared with a ridge linear regression model as a baseline, with spatial interpolation methods and with a cross-site validation experiment. When modelling without data from neighbouring stations, the RMSE for NO$_2$ ranged from 9.73 to 11.66 $μ$g/m$^3$ without traffic information, compared with 8.72 to 11.52 $μ$g/m$^3$ when traffic information was included. Additionally, for NO$_2$, SHAP analyses indicate that traffic-related variables can contribute at levels comparable to pollutant measurements from neighbouring monitoring stations in traffic-dominated~environments.