Konstantin Matchev, University of Florida

"Machine Learning Symmetries in Physics from First Principles"

Abstract: Symmetries are the cornerstones of modern theoretical physics, as they imply fundamental conservation laws. The recent boom in AI algorithms and their successful application to high-dimensional large datasets from all aspects of life motivates us to approach the problem of discovery and identification of symmetries in physics as a machine-learning task. In a series of papers, we have developed and tested a deep-learning algorithm for the discovery and identification of the continuous group of symmetries present in a labeled dataset. We use fully connected neural network architectures to model the symmetry transformations and the corresponding generators. Our proposed loss functions ensure that the applied transformations are symmetries and that the corresponding set of generators is orthonormal and forms a closed algebra. One variant of our method is designed to discover symmetries in a reduced-dimensionality latent space, while another variant is capable of obtaining the generators in the canonical sparse representation. Our procedure is completely agnostic and has been validated with several examples illustrating the discovery of the symmetries behind the orthogonal, unitary, Lorentz, and exceptional Lie groups.