Hamiltonian Neural Networks with Automatic Symmetry Detection
This work addresses the challenge of incorporating physical symmetries into data-driven models for Hamiltonian systems, which is incremental but important for improving accuracy in physics and engineering applications.
The authors tackled the problem of preserving symmetries in Hamiltonian neural networks (HNN) for learning dynamical equations by introducing a Lie algebra framework to automatically detect and embed symmetries, enabling simultaneous learning of symmetry group actions and total energy, as demonstrated on a pendulum on a cart and a two-body problem.
Recently, Hamiltonian neural networks (HNN) have been introduced to incorporate prior physical knowledge when learning the dynamical equations of Hamiltonian systems. Hereby, the symplectic system structure is preserved despite the data-driven modeling approach. However, preserving symmetries requires additional attention. In this research, we enhance HNN with a Lie algebra framework to detect and embed symmetries in the neural network. This approach allows to simultaneously learn the symmetry group action and the total energy of the system. As illustrating examples, a pendulum on a cart and a two-body problem from astrodynamics are considered.