Data-driven enhanced rough contact mechanics: PINN estimation of gap distribution across length scales for partial contacts

In this study, we employ Green’s function molecular dynamics (GFMD) to simulate non-adhesive elastic contact between a half-space and a randomly rough counterface in (1+1) dimensions, obtaining gap distributions across varying length scales and Hurst exponents. Using the GFMD-generated dataset and incorporating the convection–diffusion equation form (derived in prior and current work) as a physical constraint, we predict gap distributions via Physics-Informed Neural Network (PINN). Results demonstrate that under partial contact conditions—where analytical solutions are unavailable—PINN predictions assuming drift and diffusion coefficients scale with length exhibit high agreement with GFMD. Furthermore, PINN successfully predicts gap distributions and relative contact areas at larger scales using small-scale training data, closely matching GFMD benchmarks. This establishes PINN as an effective tool for rough surface contact problems, particularly when analytical solutions are absent or computational models are prohibitively expensive.