DeepAI
Log In Sign Up

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

10/07/2020
by   Anh Tran, et al.
0

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 (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 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 (ML) Bayesian regression model based on Gaussian processes and demonstrate the proposed methodology on two representative case studies in structure-property linkages.

READ FULL TEXT

page 4

page 11

05/17/2022

Finite Element Method-enhanced Neural Network for Forward and Inverse Problems

We introduce a novel hybrid methodology combining classical finite eleme...
02/27/2021

Unscented Kalman Inversion: Efficient Gaussian Approximation to the Posterior Distribution

The unscented Kalman inversion (UKI) method presented in [1] is a genera...
09/21/2022

An E-PINN assisted practical uncertainty quantification for inverse problems

How to solve inverse problems is the challenge of many engineering and i...
08/05/2021

Self-supervised optimization of random material microstructures in the small-data regime

While the forward and backward modeling of the process-structure-propert...
08/16/2022

Seismic fragility analysis using stochastic polynomial chaos expansions

Within the performance-based earthquake engineering (PBEE) framework, th...