Machine-learning hidden symmetries
This provides a tool for physicists and mathematicians to uncover symmetries that simplify complex systems, though it appears incremental as it applies existing neural network techniques to a new problem.
The authors tackled the problem of automatically discovering hidden symmetries, which are symmetries only apparent in a transformed coordinate system, by quantifying asymmetry through PDE violations and minimizing it using invertible neural networks. They demonstrated the method by rediscovering known symmetries like the Gullstrand-Painleve metric in black hole physics and identifying other simplifying traits.
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.