Data-driven modelling of nitrous oxide production in wastewater treatment processes using neural ordinary differential equations

Abstract

Nitrous oxide (N₂O) emissions from wastewater treatment facilities pose a significant environmental challenge. This study proposes a novel data-driven modelling approach using emerging neural ordinary differential equations (NODE) to capture the complex dynamics of N₂O production in typical activated sludge processes. The author established an experimental simulation platform, based on the BSM1 (benchmark simulation model no.1) plant, with the ASMG1 (activated sludge model for greenhouse gases no.1) mathematical model. This platform generates simulated monitoring data and validates the model. The author then proposes NODE-based models, analogous to traditional biokinetic models, capable of capturing the complex dynamics of N₂O generation through learning from process monitoring data. However, two primary challenges need to be overcome. First, to address inherent stiffness in the underlying dynamics, the author proposes a 𝗽𝗮𝗶𝗿𝗲𝗱 𝗻𝝾𝗿𝗺𝗮𝗹𝗶𝘀𝗮𝘁𝗶𝝾𝗻 𝗺𝗲𝘁𝗵𝝾𝗱 for training stability. Additionally, an 𝗶𝗻𝗰𝗿𝗲𝗺𝗲𝗻𝘁𝗮𝗹 𝘁𝗿𝗮𝗶𝗻𝗶𝗻𝗴 𝘀𝘁𝗿𝗮𝘁𝗲𝗴𝘆 was introduced, starting from a 𝗰𝝾𝗹𝗹𝝾𝗰𝗮𝘁𝗶𝝾𝗻 𝗺𝗲𝘁𝗵𝝾𝗱 to establish a robust foundation, followed by refinement using the 𝗱𝗶𝗿𝗲𝗰𝘁 𝝢𝝤𝗗𝗘 𝗺𝗲𝘁𝗵𝝾𝗱 for enhanced accuracy and efficiency. Second, as monitoring data in wastewater plants typically contain confounding factors from continuous influent variations and operational adjustments, representing 𝗲𝘅𝝾𝗴𝗲𝗻𝝾𝘂𝘀 𝗲𝘅𝗰𝗶𝘁𝗮𝘁𝗶𝝾𝗻𝘀 to the dynamics to be captured, therefore the training procedures was extended to account for these external influences. The approaches were validated on the established platform. The results demonstrate the effectiveness of the NODE-based model in capturing the intricate dynamics of N₂O production in wastewater treatment. This research presents a promising new avenue for data-driven modelling of N₂O in wastewater treatment, with the potential to improve process optimisation and emission control strategies.