Machine Learning Model to Predict Free-Energy Landscape and Position-Dependent Diffusion Constant to Extend the Scale of Dynamic Monte Carlo Simulations.

Abstract

We present a method to predict mass transport properties of large-scale heterogeneous media via coarse-grained dynamics using a dynamic Monte Carlo (MC) simulation aided by a machine learning (ML) surrogate model. The ML model was constructed to reproduce the free-energy landscape and local diffusion constant calculated by all-atom molecular dynamics (MD) simulations, aiming to efficiently evaluate these two local properties necessary for dynamic MC simulations. In this study, the ML model was built using kernel functions of descriptors representing local elemental distribution functions. The method was applied to the molecular diffusion of hydrogen in perfluorinated ionomer membranes for fuel cells, demonstrating that dynamic MC simulation using the ML model accurately reproduced the global diffusion constant across a wide range of humidity conditions, with a relative error of only 3% as compared with the original MC with the explicit position-dependent free energy and diffusion constant. On the basis of the learning curve of the ML model, even a relatively small training data set can reach a relative error of 5%. This approach is expected to be a valuable tool for elucidating mass transport mechanisms in various heterogeneous systems such as fuel cells, batteries, and biological systems.