Characterizing nanomagnetic arrays using restricted Boltzmann machines

TL;DR

This study demonstrates that restricted Boltzmann machines can effectively model complex magnetic spin systems like artificial spin ice, capturing diverse behaviors, reproducing thermodynamic properties, and distinguishing geometries even with defects.

Contribution

The paper introduces the application of restricted Boltzmann machines to analyze and differentiate complex magnetic spin systems with multiple metastable states.

Findings

RBMs capture features of artificial spin ice configurations

RBMs reproduce thermodynamic quantities away from criticality

RBMs distinguish between different geometries with defects

Abstract

Restricted Boltzmann machines are used for probabilistic learning and are capable of capturing complex dependencies in data. They are employed for diverse purposes such as dimensionality reduction, feature learning and can be used for representing and analyzing physical systems with minimal data. In this paper, we investigate a complex, strongly correlated magnetic spin system with multiple metastable states (magnetic artificial spin ice) using a restricted Boltzmann machine. Magnetic artificial spin ice is of interest because degeneracies can be specified leading to complex states that support unusual collective dynamics. We investigate two distinct geometries exhibiting different low-temperature orderings to evaluate the machine's performance and adaptability in capturing diverse magnetic behaviors. Data sets constructed with spin configurations importance-sampled from the partition function of square and pinwheel artificial spin ice Hamiltonians at different temperatures are used to extract features of distributions using a restricted Boltzmann machine. Results indicate that the restricted Boltzmann machine algorithm is sensitive to features that define the artificial spin ice configuration space and is able to reproduce the thermodynamic quantities of the system away from criticality - a feature useful for faster sample generation. Additionally, we demonstrate how the restricted Boltzmann machine can distinguish between different artificial spin ice geometries in data even when structural defects are present.