# Classifying and analysis of random composites using structural sums feature vector

## TL;DR

This paper introduces a novel feature vector based on structural sums for classifying and analyzing 2D random composites, enabling machine learning applications and geometric insights.

## Contribution

It presents a new method for representing 2D composite structures using structural sums, facilitating classification and analysis with machine learning tools.

## Key findings

- Structural sums effectively classify composite types.
- The feature vector correlates with effective conductivity.
- Irregularity measures of structures are formulated.

## Abstract

The main goal of this paper is to present the application of structural sums, mathematical objects originating from the computational materials science, in construction of a feature space vector of 2D random composites simulated by distributions of non-overlapping disks on the plane. Construction of the feature vector enables the immediate application of machine learning tools and data analysis techniques to random structures. In order to present the accuracy and the potential of structural sums as geometry descriptors, we apply them to classification problems comprising composites with circular inclusions as well as composites with shapes formed by disks. As an application, we perform the analysis of different models of composites in order to formulate the irregularity measure of random structures. We also visualize the relationship between the effective conductivity of 2D composites and the geometry of inclusions.