
Unscented Kalman Inversion: Efficient Gaussian Approximation to the Posterior Distribution
The unscented Kalman inversion (UKI) method presented in [1] is a genera...
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A probabilistic finite element method based on random meshes: Error estimators and Bayesian inverse problems
We present a novel probabilistic finite element method (FEM) for the sol...
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Statistical Treatment of Inverse Problems Constrained by Differential EquationsBased Models with Stochastic Terms
This paper introduces a statistical treatment of inverse problems constr...
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An active learning highthroughput microstructure calibration framework for solving inverse structureprocess problems in materials informatics
Determining a processstructureproperty relationship is the holy grail ...
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Selfsupervised optimization of random material microstructures in the smalldata regime
While the forward and backward modeling of the processstructurepropert...
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Sparse image reconstruction on the sphere: a general approach with uncertainty quantification
Inverse problems defined naturally on the sphere are becoming increasing...
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Polymers for Extreme Conditions Designed Using SyntaxDirected Variational Autoencoders
The design/discovery of new materials is highly nontrivial owing to the...
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Solving stochastic inverse problems for propertystructure linkages using dataconsistent inversion and machine learning
Determining processstructureproperty linkages is one of the key objectives in material science, and uncertainty quantification plays a critical role in understanding both processstructure and structureproperty 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 pushforward 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 structureproperty linkages.
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