Physics-Informed Gaussian Process Regression for Predicting ‎Flow in an Urban Drainage System ‎

Abstract

Accurate forecasting of urban drainage flows is critical for mitigating environmental pollution and optimising wastewater treatment. While purely data-driven models are computationally efficient, they often lack physical interpretation and can produce unrealistic predictions. This study proposes a probabilistic framework using physics-informed Gaussian Process Regression (GPR) to forecast Wastewater Treatment Plant inflows and Combined Sewer Overflows (CSOs). Using high-resolution sensor data from the UWO dataset in Switzerland, a naïve baseline GPR was systematically enhanced by integrating domain knowledge through composite kernel engineering, SWMM-derived prior mean functions, and strict physical output constraints. To overcome the significant computational bottleneck of exact GPs, sparsification was implemented. Furthermore, a novel stratified sparsification method was developed specifically for event-based CSO time-series to optimally allocate inducing points during rare wet-weather surges, as these events do not follow a predictable pattern that can be captured by the basic physics of the model. Results demonstrate that integrating physical constraints significantly reduces predictive error and uncertainty. Operational forecasting of upstream tank dynamics provided a robust, probabilistic early-warning trigger for CSOs that mitigates false alarms. Crucially, the stratified sparse GPR framework reduced execution times by an order of magnitude with minimal accuracy loss, offering a scalable, physics-informed tool for real-time urban drainage management.