Machine-learning hidden symmetries

TL;DR

This paper introduces an automated neural network-based approach to discover hidden symmetries in complex systems by minimizing asymmetry violations, revealing previously unrecognized symmetries and simplifying traits.

Contribution

It presents a novel method that uses invertible neural networks to identify hidden symmetries by quantifying and minimizing asymmetry violations in coordinate transformations.

Findings

Rediscovers the Gullstrand-Painleve metric with hidden translational symmetry.

Identifies hidden symmetries like Hamiltonicity and modularity.

Demonstrates effectiveness in uncovering non-traditional symmetries.

Abstract

We present an automated method for finding hidden symmetries, defined as symmetries that become manifest only in a new coordinate system that must be discovered. Its core idea is to quantify asymmetry as violation of certain partial differential equations, and to numerically minimize such violation over the space of all invertible transformations, parametrized as invertible neural networks. For example, our method rediscovers the famous Gullstrand-Painleve metric that manifests hidden translational symmetry in the Schwarzschild metric of non-rotating black holes, as well as Hamiltonicity, modularity and other simplifying traits not traditionally viewed as symmetries.