A structure-preserving neural density functional for the ions of a polymer electrolyte

Predicting the structure and response of inhomogeneous polymer electrolytes requires a description of ion correlations that retains molecular-scale accuracy while remaining transferable across spatial scales and geometries. We develop a neural density functional for electrolytes that preserves spatial symmetries, thermodynamic integrability and the Noether identities, with perfect screening recovered in stable, noncritical bulk states. Its nonlinear density dependence captures the concentration-dependent correlations missed by a pair closure, including a crossover from enhanced to suppressed long-wavelength number fluctuations at strong coupling. The functional describes density profiles at an untrained salt concentration and predicts bulk structure factors and the long-wavelength number response. Trained solely on planar density and internal-force profiles from molecular dynamics, the functional predicts ionic structure in larger domains and in two-dimensional external fields. On the same ion data, it is more accurate than three other neural density-functional architectures and keeps its accuracy with a quarter of the training runs, where the errors of the best alternative grow by about two thirds. The spatial transferability provides a necessary foundation for connecting molecular correlations to continuum predictions at larger scales.