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

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 t...

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Veröffentlicht in:JOM (1989) Jg. 73; H. 1; S. 72 - 89
Hauptverfasser: Tran, Anh, Wildey, Tim
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.01.2021
Springer Nature B.V
Schlagworte:
Alloys
Aluminum
Augmenting Physics-based Models in ICME with Machine Learning and Uncertainty Quantification
Case studies
Chemistry/Food Science
Data mining
Deep learning
Design
Earth Sciences
Engineering
Environment
Finite element method
Forward problem
Gaussian process
Homogenization
Inverse problems
Linear programming
Linkages
Localization
Machine learning
Material properties
Materials science
Microstructure
Normal distribution
Optimization
Physics
Principal components analysis
Regression models
Statistical analysis
Uncertainty
ISSN:1047-4838, 1543-1851
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Zusammenfassung: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.
Bibliographie:ObjectType-Article-1
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ISSN:1047-4838
1543-1851
DOI:10.1007/s11837-020-04432-w