Solving stochastic inverse problems for property-structure linkages using data-consistent inversion and machine learning

TL;DR

This paper introduces a probabilistic approach to identify microstructure parameter distributions that match target material properties, utilizing measure-theoretic UQ and machine learning to efficiently solve stochastic inverse problems in material science.

Contribution

It develops a data-consistent inversion framework combining measure theory, Bayesian methods, and machine learning to infer distributions of microstructure parameters from property data.

Findings

Successfully applied to two case studies in structure-property linkages.

Demonstrated reduction in computational cost using Gaussian process regression.

Provided a stable, unique solution for stochastic inverse problems.

Abstract

Determining process-structure-property linkages is one of the key objectives in material science, and uncertainty quantification plays a critical role in understanding both process-structure and structure-property linkages. In this work, we seek to learn a distribution of microstructure parameters that are consistent in the sense that the forward propagation of this distribution through a crystal plasticity finite element model (CPFEM) matches a target distribution on materials properties. This stochastic inversion formulation infers a distribution of acceptable/consistent microstructures, as opposed to a deterministic solution, which expands the range of feasible designs in a probabilistic manner. To solve this stochastic inverse problem, we employ a recently developed uncertainty quantification (UQ) framework based on push-forward probability measures, which combines techniques from measure theory and Bayes rule to define a unique and numerically stable solution. This approach requires making an initial prediction using an initial guess for the distribution on model inputs and solving a stochastic forward problem. To reduce the computational burden in solving both stochastic forward and stochastic inverse problems, we combine this approach with a machine learning (ML) Bayesian regression model based on Gaussian processes and demonstrate the proposed methodology on two representative case studies in structure-property linkages.