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

Mohammad Raeisi Gahrouei; Pedram Ramin; Vincenzo A. Riggio; Carlos Domingo-Felez

cs.LGApr 15, 2026

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

Authors: Mohammad Raeisi Gahrouei, Pedram Ramin, Vincenzo A. Riggio, Carlos Domingo-Felez

Organizations: Infrastructure and Environment, School of Engineering, University of Glasgow, University Avenue, Glasgow G12 8QQ, United Kingdom · DIATI, Politecnico di Torino, C.so Duca Degli Abruzzi, 24, 10129, Torino, Italy · PROSYS, Department of Chemical and Biochemical Engineering, Technical University of Denmark, 2800 Kgs., Lyngby, Denmark

Abstract

Model-based solutions for nitrous oxide (N2O) emissions from wastewater treatment plants (WWTP) are informed by operational datasets designed to control nutrient levels in liquid waste, coupled with dedicated campaigns for N2O measurements. We analysed how machine learning (ML) models predict disturbances to WWT operation and spatially variable N2O emissions. A real dataset was investigated to validate the modelling framework from N2O emissions predicted by four ML models (R2 = 0.79 - 0.89). Monitoring campaigns for N2O were simulated with a plant-wide mechanistic model to include additional sensors, site-level N2O datasets, and wastewater disturbances (n = 16). ML models were highly accurate (0.97 +- 0.02, n = 80), but the feature importance depended on the model, the scenario and the N2O measurement scale (reactor vs. WWTP). We argue that N2O soft sensor model predictions are limited to the measuring location and the methodological uncertainty of the dataset, which affect the interpretability of the model. Lastly, the analysis of the mechanistic model structure exposed interactions between autotrophic and heterotrophic pathways over nitric oxide which can overestimate aerobic nitrite production and bias the N2O pathway contributions.

Virtual Sensing

Virtual sensing estimates unavailable or costly-to-measure quantities from other sensor data, physical models, and learned relationships.

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Jul 26, 2026J/K move · Enter open · S save

Physics-Informed Neural Networks for Predicting Nitrous Oxide Flux

Freddy Yu, Jashanjeet Kaur Dhaliwal, Subhadeep Chakraborty

Harvard University · Department of Biosystems Engineering and Soil Science University of Tennessee · Department of Mechanical and Aerospace Engineering University of Tennessee

Climate Science Physics-Informed ML

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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.

Abstract

Virtual Sensing

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