Learning non canonical Hamiltonian systems using variational integrator
Please login to view abstract download link
In this work, we explore the application of machine learning to non-canonical Hamiltonian systems. Rather than directly learning the vector field, we follow the approach of [1], which focuses on learning both a symplectic form and a Hamiltonian, ensuring not only short-time accuracy but also long-term conservation properties like energy preservation. However, their validation relied on standard numerical methods, and we observed poor performance for large time steps when using a geometric integrator from [2]. To address this, we propose a new snapshot-based learning approach, which fits the potentials such that the geometric scheme is exact. This ensures that the learnt dynamics can be effectively integrated over long time horizons with high accuracy while preserving the system's structure. To initialize the scheme, an initial guess is produced by another neural network with no particular structure. We validate our method on problems in plasma physics, such as the guiding center model.
