# Data-Driven Microstructure Property Relations

## TL;DR

This paper develops a machine learning-based approach to predict the effective heat conductivity of heterogeneous microstructured materials from image data, emphasizing the use of 2-point correlation functions and incremental POD methods.

## Contribution

It introduces a novel combination of snapshot POD and neural networks for efficient microstructure-property prediction from images.

## Key findings

- Effective prediction accuracy demonstrated on synthetic microstructures
- Proposed incremental POD methods reduce computational complexity
- Open-source Python code available for implementation

## Abstract

An image based prediction of the effective heat conductivity for highly heterogeneous microstructured materials is presented. The synthetic materials under consideration show different inclusion morphology, orientation, volume fraction and topology. The prediction of the effective property is made exclusively based on image data with the main emphasis being put on the 2-point spatial correlation function. This task is implemented using both unsupervised and supervised machine learning methods. First, a snapshot proper orthogonal decomposition (POD) is used to analyze big sets of random microstructures and thereafter compress significant characteristics of the microstructure into a low-dimensional feature vector. In order to manage the related amount of data and computations, three different incremental snapshot POD methods are proposed. In the second step, the obtained feature vector is used to predict the effective material property by using feed forward neural networks. Numerical examples regarding the incremental basis identification and the prediction accuracy of the approach are presented. A Python code illustrating the application of the surrogate is freely available.