Machine-learning hidden symmetries

Kavli Affiliate: Max Tegmark

| First 5 Authors: Ziming Liu, Max Tegmark, , ,

| Summary:

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.

| Search Query: ArXiv Query: search_query=au:”Max Tegmark”&id_list=&start=0&max_results=10

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