Nonparametric multiscale modeling of boundary lubrication: hexadecane in highly pressurized gold asperity contacts

Abstract

Boundary lubrication is governed by molecular processes at the sliding interface that are inaccessible to classical continuum descriptions. While molecular dynamics (MD) simulations can resolve these processes in atomistic detail, incorporating their output into engineering-scale models through semi-empirical constitutive laws becomes increasingly difficult as confinement approaches the molecular scale. Here, we apply a nonparametric multiscale framework based on Gaussian process (GP) regression to model boundary lubrication of hexadecane confined between gold surfaces under pressures up to 1 GPa and gap heights down to 1.4 nm. The GP surrogates are trained on nonequilibrium MD simulations of the confined fluid and directly provide stress predictions to a continuum thin-film solver, circumventing the need for fixed-form constitutive laws. The framework naturally captures molecular phenomena such as density layering, viscosity changes, and the strongly nonlinear wall slip that dominates the frictional response at high pressures and small gap heights. Our results reproduce the atomistic benchmark data of Codrignani et al., demonstrating that nonparametric surrogate models offer a flexible and physically transparent route toward predictive continuum modeling of boundary lubrication.