Unit Operation and Process Modeling with Physics-Informed Machine Learning

Machine learning (ML) is increasingly implemented to model water infrastructure dynamics. Common ML models are primarily data-driven and require a significant amount of data for robust training. Often, obtaining robust data at higher temporal and spatial resolutions in water systems can be challenging due to cost and time considerations. In such scenarios, integrating the existing scientific knowledge into an ML model as physics-informed ML can be advantageous to enhance predictive capability and generalizability. This study examines the predictive capability and generalizability of physics-informed ML and common ML models for typical unit operation and process (UOP) system dynamics in urban water treatment. The systems studied are (1) a continuous stirred-tank reactor, (2) activated sludge reactor, and a (3) fixed-bed granular adsorption reactor. Applications of physics-informed neural networks (PINNs) are presented. Results demonstrate when the availability of data is limited: (1) common ML models are not necessarily robust for predicting water system dynamics, except when system dynamics exhibit simpler periodic patterns. Common ML models also do not generalize across different loading conditions. (2) In contrast, the developed PINN models yield high predictive capability and generalizability. (3) Benefiting from the embedded prior knowledge, PINNs require significantly reduced data sets for robust predictions. These results suggest hybridizing physics principles and domain knowledge into the ML framework can be critical for robust UOP and water systems modeling.