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

arXiv: https://arxiv.org/abs/2010.03603 · HTML: https://mlsanity.com/paper/2010.03603/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Oct 2020.

## Built on by (most cited first, 6 of 6)

- [Self-supervised optimization of random material microstructures in the small-data regime](https://mlsanity.com/paper/2108.02606/) (2021)
- [Monotonic Gaussian process for physics-constrained machine learning with materials science applications](https://mlsanity.com/paper/2209.00628/) (2022)
- [Scalable3-BO: Big Data meets HPC - A scalable asynchronous parallel high-dimensional Bayesian optimization framework on supercomputers](https://mlsanity.com/paper/2108.05969/) (2021)
- [Machine learning for structure-guided materials and process design](https://mlsanity.com/paper/2312.14552/) (2023)
- [From Displacements to Distributions: A Machine-Learning Enabled Framework for Quantifying Uncertainties in Parameters of Computational Models](https://mlsanity.com/paper/2403.03233/) (2024)
- [Copula Transformations for Data-Consistent Inversion](https://mlsanity.com/paper/2609.02832/) (2026)

## Abstract (arXiv)

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.