# Kernel methods for interpretable machine learning of order parameters

## TL;DR

This paper demonstrates that support vector machines can learn interpretable physical discriminators like order parameters from data in condensed matter physics, offering a transparent alternative to neural networks.

## Contribution

It shows that kernel methods, specifically SVMs, can identify and learn the mathematical form of physical order parameters, enhancing interpretability in phase classification tasks.

## Key findings

- SVMs successfully learned order parameters for various 2D spin models.
- Support vector machines provided interpretable decision functions.
- The approach can automate feature detection in complex physical data.

## Abstract

Machine learning is capable of discriminating phases of matter, and finding associated phase transitions, directly from large data sets of raw state configurations. In the context of condensed matter physics, most progress in the field of supervised learning has come from employing neural networks as classifiers. Although very powerful, such algorithms suffer from a lack of interpretability, which is usually desired in scientific applications in order to associate learned features with physical phenomena. In this paper, we explore support vector machines (SVMs) which are a class of supervised kernel methods that provide interpretable decision functions. We find that SVMs can learn the mathematical form of physical discriminators, such as order parameters and Hamiltonian constraints, for a set of two-dimensional spin models: the ferromagnetic Ising model, a conserved-order-parameter Ising model, and the Ising gauge theory. The ability of SVMs to provide interpretable classification highlights their potential for automating feature detection in both synthetic and experimental data sets for condensed matter and other many-body systems.