Data-driven modelling of N₂O production in wastewater processes using neural ordinary differential equations

Abstract

Modelling nitrous oxide (N₂O) production in wastewater treatment processes presents greater challenges than for other components, owing to its multiple production pathways and pronounced spatiotemporal variations. This study proposes a novel data-driven approach employing neural ordinary differential equations (NODEs) to capture the intrinsic dynamics of N₂O production in typical activated sludge processes. The NODE models are trained directly on state trajectory data, which incorporate continuous influent variations and operational adjustments as external forcings to the system dynamics. To address these external influences, we extend standard training procedures. In addition, a normalisation technique and an incremental strategy are introduced to enhance the computational efficiency of NODE implementation in stiff wastewater systems. This methodology is validated using simulated data from the benchmark simulation model no. 1 (BSM1) plant, adapted to integrate the activated sludge model for greenhouse gases no. 1 (ASMG1). Results demonstrate the efficacy of NODE-based approach in accurately capturing the complex dynamics governing N₂O production, highlighting its potential for controlling and mitigating greenhouse gases emissions in wastewater treatment.