Neural non-canonical Hamiltonian dynamics for long-time simulations
This work addresses the challenge of combining structure-preserving models and numerical schemes for long-time simulations in physics, which is incremental as it builds on prior methods to solve a specific instability issue.
The paper tackled the problem of learning non-canonical Hamiltonian dynamics from data for long-time simulations, where previous methods led to numerical instability due to gauge dependency, and proposed two training strategies that improved stability and enabled accurate long-term predictions in complex physical systems like gyrokinetic plasma physics.
This work focuses on learning non-canonical Hamiltonian dynamics from data, where long-term predictions require the preservation of structure both in the learned model and in numerical schemes. Previous research focused on either facet, respectively with a potential-based architecture and with degenerate variational integrators, but new issues arise when combining both. In experiments, the learnt model is sometimes numerically unstable due to the gauge dependency of the scheme, rendering long-time simulations impossible. In this paper, we identify this problem and propose two different training strategies to address it, either by directly learning the vector field or by learning a time-discrete dynamics through the scheme. Several numerical test cases assess the ability of the methods to learn complex physical dynamics, like the guiding center from gyrokinetic plasma physics.