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Determining process-structure-property linkages is one of the key objectivesin material science, and uncertainty quantification plays a critical role inunderstanding both process-structure and structure-property linkages. In thiswork, we seek to learn a distribution of microstructure parameters that areconsistent in the sense that the forward propagation of this distributionthrough a crystal plasticity finite element model (CPFEM) matches a targetdistribution on materials properties. This stochastic inversion formulationinfers a distribution of acceptable/consistent microstructures, as opposed to adeterministic solution, which expands the range of feasible designs in aprobabilistic manner. To solve this stochastic inverse problem, we employ arecently developed uncertainty quantification (UQ) framework based onpush-forward probability measures, which combines techniques from measuretheory and Bayes rule to define a unique and numerically stable solution. Thisapproach requires making an initial prediction using an initial guess for thedistribution on model inputs and solving a stochastic forward problem. Toreduce the computational burden in solving both stochastic forward andstochastic inverse problems, we combine this approach with a machine learning(ML) Bayesian regression model based on Gaussian processes and demonstrate theproposed methodology on two representative case studies in structure-propertylinkages.

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