Data-driven learning of 3-point correlation functions as microstructure representations

Sheng Cheng, Yang Jiao, Yi Ren

Research output: Contribution to journalArticlepeer-review


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 (100-fold smaller than the full set), and the identification of such subsets can be achieved by Bayesian optimization on a small microstructure dataset. The proposed representation can directly be used to compute material properties by leveraging the effective medium theory, allowing the construction of predictive structure-property models with significantly less data than needed by purely data-driven methods and with a computational cost 100-fold lower than the physics-based model.

Original languageEnglish (US)
Article number117800
JournalActa Materialia
StatePublished - May 1 2022
Externally publishedYes


  • Bayesian optimization
  • Heterogeneous material reconstruction
  • Higher-order spatial correlations
  • Quantitative microstructure representation

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Ceramics and Composites
  • Polymers and Plastics
  • Metals and Alloys


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