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

  • Augmenting Physics-based Models in ICME with Machine Learning and Uncertainty Quantification
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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 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 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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Acknowledgements

The views expressed in the article do not necessarily represent the views of the US Department of Energy or the US Government. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the US Department of Energy’s National Nuclear Security Administration under Contract DE-NA-0003525. This research was supported by the US Department of Energy, Office of Science, Early Career Research Program.

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This research was supported by the US Department of Energy, Office of Science, Early Career Research Program.

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  1. Optimization and Uncertainty Quantification Department, Center for Computing Research Sandia National Laboratories, Albuquerque, NM, USA

    Anh Tran & Tim Wildey

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Tran, A., Wildey, T. Solving Stochastic Inverse Problems for Property–Structure Linkages Using Data-Consistent Inversion and Machine Learning. JOM 73, 72–89 (2021). https://doi.org/10.1007/s11837-020-04432-w

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