Neural non-canonical Hamiltonian dynamics for long-time simulations

• URL: http://arxiv.org/abs/2510.01788v1
• Date: Thu, 02 Oct 2025 08:27:10 GMT
• Title: Neural non-canonical Hamiltonian dynamics for long-time simulations
• Authors: Clémentine Courtès, Emmanuel Franck, Michael Kraus, Laurent Navoret, Léopold Trémant,
• Abstract summary: This work focuses on learning non-canonical Hamiltonian dynamics from data.<n>Long-term predictions require the preservation of structure both in the learned model and in numerical schemes.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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