Generative Adversarial Symmetry Discovery

Explore the innovative LieGAN framework for automatic symmetry discovery in this comprehensive lecture. Delve into the world of equivariant neural networks and their applications in scientific fields, understanding how LieGAN relaxes the constraint of knowing symmetry groups a priori. Learn how the framework employs a generative adversarial training approach to uncover equivariances from datasets, representing symmetry as an interpretable Lie algebra basis. Discover the framework's capability to identify various symmetries, including rotation groups and restricted Lorentz groups, in trajectory prediction and top-quark tagging tasks. Examine how LieGAN extends to uncovering nonlinear symmetries in high-dimensional dynamics. Gain insights into the practical applications of learned symmetries in improving prediction accuracy, generalization, symbolic equation discovery, and long-term forecasting for diverse dynamical systems.