Operator learning for urban water clarification hydrodynamics and particulate matter transport with physics-informed neural networks

Abstract

Computational fluid dynamics (CFD) can be a powerful tool for higher-fidelity water infrastructure planning and design. Despite decades of development and demonstration over a wide range of water systems such as clarification basins, activated sludge processes, ozone contactors, etc., CFD remains primarily used in academic research, with limited application in civil and environmental engineering practice. This limitation is contributed by its higher computational cost and demand for specialized user skills. This, however, need not be the case, if a robust and efficient surrogate model can be developed from CFD simulations and independently deployed for engineering purposes. Leveraging the emerging scientific machine learning (ML) techniques of physics-informed ML and operator learning, this study develops a composite neural network (CPNN) for learning the flow hydrodynamics and particulate matter (PM) transport and fate in clarification systems. The CPNN consists of a deep operator network (DeepONet) as an encoder and a physics-informed neural network (PINN) as a decoder. In contrast to common "black box" and lumped ML approaches, the developed CPNN directly incorporates physics principles into its architecture. Furthermore, the CPNN is designed for process-resolved and operator learning, enabling it to predict spatial hydrodynamics and PM concentration distribution (i.e., contours) across different basin geometrics and loading conditions. Compared to CFD simulation, the developed CPNN model has significantly higher computational efficiency (∼ milliseconds) while demonstrating robust predictive capability. For predicting basin hydrodynamics across 10,000 test cases, the trained CPNN model achieves an R² above 0.8 for 66.4% of cases and an R² above 0.4 for 89.2% of cases. A similar performance is also demonstrated by the CPNN in predicting basin PM concentration. Further investigation reveals that basin geometrics that trigger bi-modal flow solutions can be particularly challenging for ML. Additionally, this study visualizes the dependency of basin hydrodynamics and PM concentration on basin geometrics and loading conditions, providing valuable insights for optimizing basin configuration. Lastly, the potentials and benefits of web-based applications, e.g., DeepXtorm, as a user-friendly interface for the developed CPNN model is discussed. This study represents the initial step toward achieving real-time higher-fidelity water infrastructure planning, design, optimization, and regulation.

Keywords: CFD; Operator learning; Particulate matter; Stormwater; Water infrastructure; Water treatment.