Neural non-canonical Hamiltonian dynamics for long-time simulations
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Abstract (arXiv)
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.
Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 27 of its 50 references that are in the map. First posted on arXiv 2 Oct 2025.
Builds on
27 of 50 references.
References · 27
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15 more
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- 2024Symplectic Neural Networks Based on Dynamical Systemscited by 4
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Citing papers per year: 2026: 2.
2 papers.