Atomistic simulation assisted error-inclusive Bayesian machine learning for probabilistically unraveling the mechanical properties of solidified metals

Abstract

Solidification phenomenon has been an integral part of the manufacturing processes of metals, where the quantification of stochastic variations and manufacturing uncertainties is critically important. Accurate molecular dynamics (MD) simulations of metal solidification and the resulting properties require excessive computational expenses for probabilistic stochastic analyses where thousands of random realizations are necessary. The adoption of inadequate model sizes and time scales in MD simulations leads to inaccuracies in each random realization, causing a large cumulative statistical error in the probabilistic results obtained through Monte Carlo (MC) simulations. In this work, we present a machine learning (ML) approach, as a data-driven surrogate to MD simulations, which only needs a few MD simulations. This efficient yet high-fidelity ML approach enables MC simulations for full-scale probabilistic characterization of solidified metal properties considering stochasticity in influencing factors like temperature and strain rate. Unlike conventional ML models, the proposed hybrid polynomial correlated function expansion here, being a Bayesian ML approach, is data efficient. Further, it can account for the effect of uncertainty in training data by exploiting mean and standard deviation of the MD simulations, which in principle addresses the issue of repeatability in stochastic simulations with low variance. Stochastic numerical results for solidified aluminum are presented here based on complete probabilistic uncertainty quantification of mechanical properties like Young’s modulus, yield strength and ultimate strength, illustrating that the proposed error-inclusive data-driven framework can reasonably predict the properties with a significant level of computational efficiency.