  Species transport models typically combine partial differential equations
(PDEs) with relations from hindered transport theory to quantify
electromigrative, convective, and diffusive transport through complex
nanoporous systems; however, these formulations are frequently substantial
simplifications of the governing dynamics, leading to the poor generalization
performance of PDE-based models. Given the growing interest in deep learning
methods for the physical sciences, we develop a machine learning-based approach
to characterize ion transport across nanoporous membranes. Our proposed
framework centers around attention-enhanced neural differential equations that
incorporate electroneutrality-based inductive biases to improve generalization
performance relative to conventional PDE-based methods. In addition, we study
the role of the attention mechanism in illuminating physically-meaningful
ion-pairing relationships across diverse mixture compositions. Further, we
investigate the importance of pre-training on simulated data from PDE-based
models, as well as the performance benefits from hard vs. soft inductive
biases. Our results indicate that physics-informed deep learning solutions can
outperform their classical PDE-based counterparts and provide promising avenues
for modelling complex transport phenomena across diverse applications.
