Machine Learning Lie Structures & Applications to Physics

TL;DR

This paper demonstrates that machine learning can significantly accelerate the computation of tensor products and branching rules of Lie algebra representations, which are fundamental in understanding symmetries in physics.

Contribution

It introduces a machine learning approach to efficiently compute tensor products and branching rules of Lie algebra representations, outperforming traditional algorithms.

Findings

ML achieves orders of magnitude speed-up in computations

ML accurately predicts tensor product decompositions

Applicable to classical and exceptional Lie algebras

Abstract

Classical and exceptional Lie algebras and their representations are among the most important tools in the analysis of symmetry in physical systems. In this letter we show how the computation of tensor products and branching rules of irreducible representations are machine-learnable, and can achieve relative speed-ups of orders of magnitude in comparison to the non-ML algorithms.