Enhancing mechanistic models with neural differential equations to predict electrodialysis fouling

Abstract Fouling of the ion-exchange membranes by colloidal substances present in bio-based process streams is an important hurdle for electrodialysis. The development of a model is challenged by the limited availability of experimental data and the complexity of the underlying physics. This research addresses this challenge by combining a mechanistic description of the transport processes with a machine learning model to describe the complex phenomena of colloidal aggregation and attachment to the surface of ion-exchange membranes. After validation with fouling experiments using acrylamide as colloidal foulant, it was found that this hybrid model improves the predictive power of the model while reducing the need for experimental data. An analysis of both mechanistic and machine learning models showed that the attachment probability of anion polyacrylamide (APAM) is influenced by the current density and the size of the fouling layer in a non-linear manner. An increase in current density leads to an increase in the attachment probability while the opposite holds for the size of the fouling layer. This research shows that machine learning can complement mechanistic models where fundamental knowledge is lacking or computational resources are limiting. The combination maintains the interpretability and generalisability of mechanistic models while harnessing the accuracy of machine learning.