Solving Stochastic Inverse Problems for Property–Structure Linkages Using Data-Consistent Inversion and Machine Learning

Tran, Anh; Wildey, Tim

doi:10.1007/s11837-020-04432-w

Title: Solving Stochastic Inverse Problems for Property–Structure Linkages Using Data-Consistent Inversion and Machine Learning

Journal Article · Fri Nov 20 00:00:00 EST 2020 · JOM. Journal of the Minerals, Metals & Materials Society

DOI:https://doi.org/10.1007/s11837-020-04432-w· OSTI ID:1760459

^[1]; Wildey, Tim ^[1]

Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States). Center for Computing Research

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 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. Furthermore, to solve this stochastic inverse problem, we employ a recently developed uncertainty quantification 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 Bayesian regression model based on Gaussian processes and demonstrate the proposed methodology on two representative case studies in structure–property linkages.

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Research Organization:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000; NA0003525

OSTI ID:: 1760459

Report Number(s):: SAND-2020-10928J; 691277

Journal Information:: JOM. Journal of the Minerals, Metals & Materials Society, Vol. 73, Issue 1; ISSN 1047-4838

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

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