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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.00576 |
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Table of Contents:
- Hamiltonian systems lie at the heart of modeling the physical world. Their defining scalar, the Hamiltonian, encodes both energy conservation and symplectic geometry in its phase-space trajectories. Recent deep learning approaches model Hamiltonian systems by embedding their properties either in the architecture or in the loss function. However, they typically ignore that: i) a Hamiltonian carries units of energy and/or ii) that every integrable Hamiltonian admits a canonical transformation to action-angle coordinates in which the dynamics reduce to a simple rotation on an invariant torus. We propose BuSyNet, a deep learning architecture that combines these two constraints via a dimensionally-consistent, symplectic transformation. A symplectic layer maps input trajectories to lower-dimensional latent action-angle variables, which are then combined with system parameters to discover a symbolic Hamiltonian expression in units of energy. Evaluated on the harmonic oscillator and the Kepler two-body problem (in 2D and 3D), BuSyNet recovers concise, closed-form Hamiltonians that outperform state-of-the-art neural architectures in long-term prediction accuracy and stability, while maintaining interpretability.