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

Abstract

Accurate forecasting of urban drainage flows is critical for optimising wastewater treatment. While data-driven models are computationally efficient, they often lack physical interpretation. This study proposes a physics-constrained Gaussian Process Regression (GPR) framework to forecast Wastewater Treatment Plant inflows and Combined Sewer Overflows (CSOs) using the UWO dataset in Switzerland. The baseline GPR was enhanced through composite kernel engineering, SWMM-derived prior mean functions, and physical output constraints bounding the posterior function to possible values. To overcome computational bottlenecks, a novel stratified sparsification method was developed to optimally allocate inducing points during rare wet-weather surges when CSOs happen. Results demonstrate that physical constraints significantly reduce predictive error and uncertainty, providing robust probabilistic early warnings. Crucially, the stratified sparse framework reduced execution times by an order of magnitude with minimal accuracy loss, offering a scalable, physics-constrained tool for real-time urban drainage management.