Department of Computer Engineering

Symmetry groups are crucial constructs for understanding the behavior of pure mathematical or physical systems governed by differential equations. We have developed a framework capable of learning continuous group symmetries in the context of Lie point and contact transformations. The key idea in the proposed method is to build the symmetry group G by learning the relevant exp map, which is a crucial element in the study of Lie groups. The exp for G is implicitly learned through the vector fields that span the associated Lie algebra g. Unlike previous algebraic approaches, our iterative method is analytical and based on the moving (co)frame method to construct the invariant (co)frame for the equivalence problem induced by the given differential equations. In our experiments, we validate the integrity of these learned vector fields by demonstrating their generalization to various solution domains beyond the training domain. Furthermore, the framework offers an optimal way to transform one solution to another via exp . Finally, we illustrate how group symmetries can be leveraged to simplify a differential equation system defined on a manifold that is immersed in a particular jet space.