Development of physics-informed machine-learning models to enhance understanding and prediction of membrane fouling

Although membrane technology is a promising separation means due to the relatively low energy requirement and amenability for continuous operation, more widespread implementation persists to be plagued by the inevitable membrane-fouling phenomena. To enable predictions of flux decline, the Hermia laws have laid out four governing equations for the four basic fouling mechanisms more than four decades ago, and subsequently combined fouling models have provided more complex equations that account for two to three fouling mechanisms simultaneously. More recently, data-driven black-box machine-learning models that do not require any physical equations have improved understanding and predictions. To leverage the benefits of physical laws to govern the right trends, physics-informed machine-learning models have gained much momentum. Here, the four Hermia fouling equations were hybridized with neural networks to develop a physics-informed neural network (PINN) architecture to enhance mechanistic understandings from flux-decline data and enable more accurate predictions of flux decline. A comprehensive dataset consisting of over 50 flux decline curves from more than 10 studies was compiled. Firstly, the relative dominance of the four fouling mechanisms in influencing flux decline was quantified, allowing direct knowledge of which is most operative. This was enabled by applying a fractional weighing factor to each of the mechanisms and employing neural network to best-fit the empirical data to the resulting equation. Secondly, more accurate predictions of flux decline even with a much-reduced dataset was enabled by a PINN model, which dynamically assigns weights to all four fouling mechanisms to embed the physical laws into the learning process. This study demonstrates the potential of physics-informed machine-learning models in significantly augmenting the understanding, prediction and operation of membrane-filtration processes. • Develop physics-informed machine-learning models for membrane fouling. • Hybridize neural network with Hermia fouling equations to adhere to physical laws. • Evaluate over 50 flux-decline curves from 10 different studies. • Quantify relative roles of the four fouling mechanisms in influencing flux decline. • Prediction accuracy outperforms black-box models even with reduced dataset.