Symmetry Discovery using Machine Learning

The discovery of symmetries in physical laws is of both pure and applied interest to various areas of physics. Besides being meaningful in and of itself, symmetry identification in a data set magnifies the statistical power of the data set by reducing its effective dimension. We propose a customised loss function for a modified generative adversarial network (GAN) to allow the neural net to discover non--trivial symmetries in data sets. The loss function and the associated neural net are analysed both analytically and experimentally to study their ability to discover non--trivial symmetries. The loss function we propose is specific yet flexible, and may be adjusted to reflect various symmetry groups by a suitable choice of the mean squared error term.