# Data-Driven Learning of 3-Point Correlation Functions as Microstructure Representations

arXiv: https://arxiv.org/abs/2109.02255 · HTML: https://mlsanity.com/paper/2109.02255/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 51 references that are in the map.
- First posted on arXiv 6 Sep 2021.

## Builds on (most cited first, 3 of 3)

- [A Transfer Learning Approach for Microstructure Reconstruction and Structure-property Predictions](https://mlsanity.com/paper/1805.02784/) (2018)
- [Microstructure Representation and Reconstruction of Heterogeneous Materials via Deep Belief Network for Computational Material Design](https://mlsanity.com/paper/1612.07401/) (2016)
- [Infill Optimization for Additive Manufacturing -- Approaching Bone-like Porous Structures](https://mlsanity.com/paper/1608.04366/) (2016)

## Built on by (most cited first, 1 of 1)

- [PolyMicros: Bootstrapping a Foundation Model for Polycrystalline Material Structure](https://mlsanity.com/paper/2506.11055/) (2025)

## Abstract (arXiv)

This paper considers the open challenge of identifying complete, concise, and explainable quantitative microstructure representations for disordered heterogeneous material systems. Completeness and conciseness have been achieved through existing data-driven methods, e.g., deep generative models, which, however, do not provide mathematically explainable latent representations. This study investigates representations composed of three-point correlation functions, which are a special type of spatial convolutions. We show that a variety of microstructures can be characterized by a concise subset of three-point correlations, and the identification of such subsets can be achieved by Bayesian optimization. Lastly, we show that the proposed representation can directly be used to compute material properties based on the effective medium theory.