Machine Learning Symmetry Discovery for Integrable Hamiltonian Dynamics
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911383229038592 |
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| author | Hou, Wanda Li, Molan You, Yi-Zhuang |
| author_facet | Hou, Wanda Li, Molan You, Yi-Zhuang |
| contents | We propose a data-driven Machine-Learning Symmetry Discovery (MLSD) framework for identifying continuous symmetry generators and their Lie-algebraic structure directly from phase-space trajectory data expressed in canonical coordinates. MLSD parameterizes candidate conserved quantities with neural networks and learns antisymmetric structure coefficients by enforcing Poisson-bracket closure, supplemented by a weak independence regularizer. We validate MLSD on two integrable benchmark systems -- the three-dimensional Kepler problem and the three-dimensional isotropic harmonic oscillator -- recovering the expected non-Abelian algebras (respectively $\mathfrak{so}(4)$ and $\mathfrak{su}(3)$) up to basis transformations. This work focuses on integrable benchmark dynamics, where global conserved quantities are well-defined and admit compact representations learnable from canonical-coordinate trajectories. Extending symmetry discovery to mixed or chaotic phase-space regimes is an important direction for future work. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_14632 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Machine Learning Symmetry Discovery for Integrable Hamiltonian Dynamics Hou, Wanda Li, Molan You, Yi-Zhuang Disordered Systems and Neural Networks Classical Physics Data Analysis, Statistics and Probability We propose a data-driven Machine-Learning Symmetry Discovery (MLSD) framework for identifying continuous symmetry generators and their Lie-algebraic structure directly from phase-space trajectory data expressed in canonical coordinates. MLSD parameterizes candidate conserved quantities with neural networks and learns antisymmetric structure coefficients by enforcing Poisson-bracket closure, supplemented by a weak independence regularizer. We validate MLSD on two integrable benchmark systems -- the three-dimensional Kepler problem and the three-dimensional isotropic harmonic oscillator -- recovering the expected non-Abelian algebras (respectively $\mathfrak{so}(4)$ and $\mathfrak{su}(3)$) up to basis transformations. This work focuses on integrable benchmark dynamics, where global conserved quantities are well-defined and admit compact representations learnable from canonical-coordinate trajectories. Extending symmetry discovery to mixed or chaotic phase-space regimes is an important direction for future work. |
| title | Machine Learning Symmetry Discovery for Integrable Hamiltonian Dynamics |
| topic | Disordered Systems and Neural Networks Classical Physics Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2412.14632 |