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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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| _version_ | 1866912994994159616 |
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| author | Germany, Joe Bakarji, Joseph Najem, Sara |
| author_facet | Germany, Joe Bakarji, Joseph Najem, Sara |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00576 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Discovery of Symbolic Hamiltonian Expressions with Buckingham-Symplectic Networks Germany, Joe Bakarji, Joseph Najem, Sara Computational Physics Exactly Solvable and Integrable Systems Data Analysis, Statistics and Probability 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. |
| title | Discovery of Symbolic Hamiltonian Expressions with Buckingham-Symplectic Networks |
| topic | Computational Physics Exactly Solvable and Integrable Systems Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2604.00576 |