Visual Machine Learning: Insight through Eigenvectors, Chladni patterns and community detection in 2D particulate structures

TL;DR

This paper explores how unsupervised machine learning techniques applied to 2D particulate systems reveal insights connecting classical and quantum mechanical features, enhancing understanding of physical systems.

Contribution

It introduces a framework using eigenvector analysis and community detection to interpret ML features in physical systems, demonstrating their deep connection to quantum mechanics.

Findings

Eigenvector features relate to quantum solutions

Community detection reveals structural insights

ML techniques bridge classical and quantum physics

Abstract

Machine learning (ML) is quickly emerging as a powerful tool with diverse applications across an extremely broad spectrum of disciplines and commercial endeavors. Typically, ML is used as a black box that provides little illuminating rationalization of its output. In the current work, we aim to better understand the generic intuition underlying unsupervised ML with a focus on physical systems. The systems that are studied here as test cases comprise of six different 2-dimensional (2-D) particulate systems of different complexities. It is noted that the findings of this study are generic to any unsupervised ML problem and are not restricted to materials systems alone. Three rudimentary unsupervised ML techniques are employed on the adjacency (connectivity) matrix of the six studied systems: (i) using principal eigenvalue and eigenvectors of the adjacency matrix, (ii) spectral decomposition, and (iii) a Potts model based community detection technique in which a modularity function is maximized. We demonstrate that, while solving a completely classical problem, ML technique produces features that are distinctly connected to quantum mechanical solutions. Dissecting these features help us to understand the deep connection between the classical non-linear world and the quantum mechanical linear world through the kaleidoscope of ML technique, which might have far reaching consequences both in the arena of physical sciences and ML.