A physics-informed neural network for interpretable membrane-fouling prediction with adaptive transitions between fouling mechanisms

Membrane fouling remains a major challenge in filtration processes, causing flux decline, reduced efficiency, and higher operational costs. Classical models such as the Hermia blocking laws describe idealized single fouling mechanisms but fail to capture the complex, dynamic transitions that occur in practical systems. Combined or empirical models offer more realism but often suffer from non-unique parameter fitting and limited interpretability, reducing their predictive reliability. Recent advances in machine learning (ML) have improved predictive accuracy, yet purely data-driven approaches lack physical grounding and require extensive datasets. To bridge this gap, we propose a Physics-Informed Neural Network (PINN) that integrates the four classical Hermia fouling mechanisms – complete pore blockage, intermediate blockage, pore constriction, and cake filtration - within a single, physically constrained data-driven model. The PINN employs adaptive sigmoid weighting functions for smooth and continuous transitions between filtration stages, and a probabilistic loss formulation that balances data fidelity, physical constraints, and initial conditions through adaptive weights. Validated on a diverse dataset encompassing multiple membrane types, transmembrane pressures, and feed conditions, the model accurately identifies stage transitions and quantifies the relative contribution of each fouling mechanism. The developed PINN achieves high predictive accuracy with low uncertainty, outperforming classical fouling models while offering mechanistic interpretability and a physically consistent basis for membrane-fouling prediction. • PINN embeds Hermia's laws to model microfiltration fouling mechanistically. • Smooth sigmoid transitions facilitate gradual shifts between fouling stages. • Adaptive weighting balances data, physics, and initial conditions. • Model estimates stage transition times and quantifies mechanism weights. • Validated on diverse cases, PINN yields accurate, low-uncertainty predictions.