Neural network surrogates enable robust and accessible modeling of renal epithelial transport

Mathematical models of renal epithelial transport provide powerful tools for investigating kidney function, but their broader use is often hindered by numerical challenges. These highly nonlinear model equations typically require specialized solvers and careful initialization, which can reduce robustness and accessibility. To address these limitations, we propose a neural-network (NN)-based framework for approximating steady-state solutions of epithelial transport models. Training and validation data are generated using published mechanistic models by systematically varying transport parameters and computing corresponding cellular states, including solute concentrations, membrane potentials, and fluxes. The NN is then trained as a fast surrogate for the mechanistic model. Once trained, the NN accurately predicts cellular variables for previously unseen parameter sets. Using proximal convoluted tubule and medullary thick ascending limb cells as examples, we demonstrate high predictive accuracy when training and testing data are drawn from the same sex. Cross-sex predictions are less accurate, reflecting known sex differences in transporter abundance. The NN also accurately models transporter inhibition scenarios and can be trained to infer membrane transport properties from measurable physiological data, highlighting its potential for inverse modeling. Overall, this NN-based solver provides a robust alternative to traditional approaches, eliminating convergence failures and improving accessibility of epithelial transport models.