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Neural Symplectic Form: Learning Hamiltonian Equations on General Coordinate Systems
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| learn symplectic 1-form (neural symplectic form) instead of a free skew matrix | Skew Matrix Learning · double pendulum | test time-derivative error: 8.47 ± 1.22 -> 4.02 ± 2.08 | Helped |
| learn symplectic 1-form instead of a free skew matrix | Skew Matrix Learning · mass-spring | test time-derivative error: 102.07 ± 68.00 -> 0.52 ± 0.71 | Helped |
| learn symplectic 1-form instead of a free skew matrix | Skew Matrix Learning · Lotka-Volterra | energy error: 0.041 ± 0.072 -> 0.012 ± 0.013 | Helped |
| use neural symplectic form instead of HNN on non-canonical coordinates | HNN · double pendulum | test time-derivative error: 15.69 ± 0.44 -> 4.02 ± 2.08 | Helped |
| use neural symplectic form instead of HNN | HNN · Lotka-Volterra | test time-derivative error: 227.03 ± 2.31 -> 0.46 ± 0.30 | Helped |
| use neural symplectic form instead of NODE | NODE · double pendulum (T=30) | energy error: 11.240 ± 12.297 -> 7.300 ± 3.925 | Helped |
| use neural symplectic form instead of NODE | NODE · mass-spring | test time-derivative error: 0.17 ± 0.14 -> 0.52 ± 0.71 | No clear effect |
| use neural symplectic form instead of NODE | NODE · Lotka-Volterra | energy error: 0.578 ± 0.558 -> 0.012 ± 0.013 | Helped |
| use neural symplectic form instead of HNN | HNN · mass-spring | energy error: 0.551 ± 0.112 -> 0.368 ± 0.055 | No clear effect |
| use neural symplectic form instead of HNN | HNN · double pendulum (T=5) | energy error: (0.755 ± 0.320) -> 6.400 ± 0.971 | Hurt |
| use neural symplectic form instead of LNN | LNN · mass-spring | test time-derivative error: 882.52 ± 1753.93 -> 0.52 ± 0.71 | Helped |
| use neural symplectic form instead of HNN on image latent features | HNN · image-based dynamics | final test loss: 0.161 -> 0.060 | Helped |
Closest papers by meaning
- Data-driven Prediction of General Hamiltonian Dynamics via Learning Exactly-Symplectic Maps (ICML 2021 · similarity 0.90)
- Symplectic ODE-Net: Learning Hamiltonian Dynamics with Control (ICLR 2020 · similarity 0.89)
- Nonseparable Symplectic Neural Networks (ICLR 2021 · similarity 0.89)
- Towards Cross Domain Generalization of Hamiltonian Representation via Meta Learning (ICLR 2024 · similarity 0.86)
- Hamiltonian Neural PDE Solvers through Functional Approximation (NeurIPS 2025 · similarity 0.84)
- Context-Informed Neural ODEs Unexpectedly Identify Broken Symmetries: Insights from the Poincaré–Hopf Theorem (ICML 2025 · similarity 0.84)
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