Physics-Guided Machine Learning with Roughness-Corrected Interfacial Descriptors for Membrane Fouling Prediction

Abstract

Membrane fouling remains a critical challenge in the design, optimization, and long-term stability of membrane-based water treatment technologies. However, reliable prediction of fouling behavior is hindered by the complex membrane-foulant interfacial interactions induced by membrane surface roughness. This study presents a two-stage physics-guided machine learning (ML) framework to improve fouling prediction. In the first stage, a residual learning model was developed to capture deviations from the ideal smooth-surface assumption in the extended Derjaguin–Landau–Verwey–Overbeek (XDLVO) theory, thereby generating roughness-corrected interfacial descriptors. In the second stage, these descriptors were incorporated into an ML model to predict the flux decline ratio (FDR) and flux recovery ratio (FRR) using an experimental data set comprising 162 membranes and 68 foulants. The model utilizing roughness-corrected interfacial descriptors consistently outperformed those using uncorrected interfacial descriptors and purely data-driven approaches. Under repeated random train-test splits, the model achieved average absolute errors below 7%, whereas group-based validation revealed reduced extrapolation performance, particularly for unseen foulants. Model interpretation further identified Lifshitz-van der Waals interactions (ΔGLW) and electrostatic interactions (ΔGEL) as the key contributors among the interfacial descriptors to FDR and FRR predictions, respectively, with lower predicted FDR and higher predicted FRR generally associated with systems exhibiting ΔGLW values above −1994 ± 88 kT and ΔGEL values below 250 ± 8 kT within the current data set.