Probabilistic prediction of stress–strain curves at the nanoscale: A multi-output Gaussian process approach with molecular dynamics simulations

Abstract

This study introduces a novel two-step approach for the probabilistic prediction of stress–strain curves of materials at the nanoscale, specifically in terms of material volume. Molecular dynamics (MD) simulations are first conducted for materials of varying sizes to acquire stress–strain data. A multioutput Gaussian process with Bayesian analysis is then employed to model the stress–strain behavior and predict stress and strain values at critical deformation points (i.e., yielding, hardening, and failure) for different material sizes. By incorporating comprehensive uncertainty estimates alongside the probabilistic predictions, this probabilistic machine learning algorithm enables precise forecasting of the stress–strain behavior of materials beyond the typical material volume range covered by MD simulations, addressing the critical inherent size limitations issue in atomistic simulations. In this study, the effectiveness of the method is rigorously validated using pure copper, which possesses abundant experimental stress–strain data. However, the methodology is not limited to a specific material and can serve as a robust and versatile tool for probabilistic prediction of the mechanical behavior of materials at the nanoscale across various applications in the field of materials science and engineering.