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

arXiv: https://arxiv.org/abs/2108.02606 · HTML: https://mlsanity.com/paper/2108.02606/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 59 references that are in the map.
- First posted on arXiv 5 Aug 2021.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Gaussian Process Kernels for Pattern Discovery and Extrapolation](https://mlsanity.com/paper/1302.4245/) (2013)
- [Online Deep Learning: Learning Deep Neural Networks on the Fly](https://mlsanity.com/paper/1711.03705/) (2017)
- [Bayesian optimization for materials design](https://mlsanity.com/paper/1506.01349/) (2015)
- [Bayesian Optimization for Materials Design with Mixed Quantitative and Qualitative Variables](https://mlsanity.com/paper/1910.01688/) (2019)
- [Microstructure Representation and Reconstruction of Heterogeneous Materials via Deep Belief Network for Computational Material Design](https://mlsanity.com/paper/1612.07401/) (2016)
- [Solving stochastic inverse problems for property-structure linkages using data-consistent inversion and machine learning](https://mlsanity.com/paper/2010.03603/) (2020)
- [Bayesian model and dimension reduction for uncertainty propagation: applications in random media](https://mlsanity.com/paper/1711.02475/) (2017)

## Built on by (most cited first, 4 of 4)

- [Data-Driven Design for Metamaterials and Multiscale Systems: A Review](https://mlsanity.com/paper/2307.05506/) (2023)
- [Physics-Aware Neural Implicit Solvers for multiscale, parametric PDEs with applications in heterogeneous media](https://mlsanity.com/paper/2405.19019/) (2024)
- [A Primer on Variational Inference for Physics-Informed Deep Generative Modelling](https://mlsanity.com/paper/2409.06560/) (2024)
- [MatSAM: Efficient Extraction of Microstructures of Materials via Visual Large Model](https://mlsanity.com/paper/2401.05638/) (2024)

## Abstract (arXiv)

While the forward and backward modeling of the process-structure-property chain has received a lot of attention from the materials community, fewer efforts have taken into consideration uncertainties. Those arise from a multitude of sources and their quantification and integration in the inversion process are essential in meeting the materials design objectives. The first contribution of this paper is a flexible, fully probabilistic formulation of such optimization problems that accounts for the uncertainty in the process-structure and structure-property linkages and enables the identification of optimal, high-dimensional, process parameters. We employ a probabilistic, data-driven surrogate for the structure-property link which expedites computations and enables handling of non-differential objectives. We couple this with a novel active learning strategy, i.e. a self-supervised collection of data, which significantly improves accuracy while requiring small amounts of training data. We demonstrate its efficacy in optimizing the mechanical and thermal properties of two-phase, random media but envision its applicability encompasses a wide variety of microstructure-sensitive design problems.