  Continuum models for ion transport through polyamide nanopores require
solving partial differential equations (PDEs) through complex pore geometries.
Resolving spatiotemporal features at this length and time-scale can make
solving these equations computationally intractable. In addition, mechanistic
models frequently require functional relationships between ion interaction
parameters under nano-confinement, which are often too challenging to measure
experimentally or know a priori. In this work, we develop the first
physics-informed deep learning model to learn ion transport behaviour across
polyamide nanopores. The proposed architecture leverages neural differential
equations in conjunction with classical closure models as inductive biases
directly encoded into the neural framework. The neural differential equations
are pre-trained on simulated data from continuum models and fine-tuned on
independent experimental data to learn ion rejection behaviour. Gaussian noise
augmentations from experimental uncertainty estimates are also introduced into
the measured data to improve model generalization. Our approach is compared to
other physics-informed deep learning models and shows strong agreement with
experimental measurements across all studied datasets.
