Explainable hybrid modeling of nitrous oxide emissions in wastewater treatment: Integrating mechanistic knowledge with uncertainty-aware machine learning.

Mechanistic models for nitrous oxide (N2O) emissions from wastewater treatment plants often suffer from over-parameterization, while machine-learning lacks interpretability. To address these limitations, this study introduces a novel explainable hybrid framework integrating mechanistic models with Long Short-Term Memory (LSTM) and Gaussian Process (GP) regression. Adopting a serial-parallel architecture, this work represents the first application of GP for N2O modeling, enabling robust uncertainty quantification for limited datasets via Bayesian inference. The hybrid model achieved remarkable accuracy (R2 > 0.99 %) for total N2O estimation, reducing mean absolute error by 66.4 % and 47.8 % compared to LSTM and LSTM-based hybrids, respectively. SHapley Additive exPlanations (SHAP) method analysis identified air flux as a pivotal factor (contribution > 0.4). By coupling mechanistic insights with data-driven uncertainty analysis, this framework exhibits robust generalization across diverse operational conditions, offering a significant methodological advancement toward interpretable, uncertainty-aware greenhouse gas mitigation in wastewater treatment.