Data-Driven, Quasi-continuum Theory for Confined Fluids at the Nanoscale

We present a data-efficient, multiscale framework for predicting the density profiles of confined water at the nanoscale. When quantum effects are neglected, classical molecular dynamics simulations often yield inaccurate predictions for strong confinement, while ab initio molecular dynamics (AIMD) simulations require prohibitively long timescales for accurate density estimates. To address this, we train Allegro, a graph neural network interatomic potential, on three datasets: confined water in graphene channels (1 to 4 nm), bulk state, and the interface (where fluid properties are influenced by a single wall). The learned potential is used to generate sufficient statistics to train a denoising diffusion model, which transforms noisy force profiles into smooth ones. Using the learned potential and a classification scheme that categorizes atomic neighborhoods as bulk, interface, or confinement, the average force profile for a given channel width based on limited AIMD data is obtained. The resulting noisy profiles are smoothened by the diffusion model, and these smooth forces are then linked to continuum theory via the Nernst-Planck equation to compute density profiles across channel widths ranging from a few atomic diameters up to lengths inaccessible to ab initio methods. Our framework offers a data-efficient and computationally cheap method to bridge ab initio physics with continuum theory for predicting density profiles of confined fluids.