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Data-driven Prediction of General Hamiltonian Dynamics via Learning Exactly-Symplectic Maps
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Learn the evolution map through a generating function, ensuring exact symplecticity | GFNN · Integrable Hamiltonian dynamics | long-time trajectory prediction error growth | Helped |
| Use GFNN instead of the tested alternatives | 2-Body Problem · 2-Body Problem | semi-major axis and eccentricity prediction error | Helped |
| Use GFNN instead of HNN for a regular trajectory | Hénon-Heiles · Hénon-Heiles, regular non-periodic trajectory | trajectory prediction error growth | Helped |
| Use GFNN instead of the tested alternatives | Hénon-Heiles · Hénon-Heiles, chaotic orbit | KL divergence from the true empirical distribution | Helped |
| Use GFNN instead of the tested alternatives | PCR3BP · PCR3BP, nearly-integrable regime | trajectory prediction error | Helped |
| Use GFNN instead of the tested alternatives | Standard Map · Standard Map, chaotic sea | KL divergence from the true empirical distribution | Helped |
| Learn the discrete evolution map directly rather than fitting a vector field or Hamiltonian | GFNN · Standard Map, chaotic sea | capture of major regular islands | Helped |
| Use GFNN instead of the tested alternatives | Standard Map · Standard Map, regular islands | capture of quasiperiodic orbits | Helped |
| Apply GFNN to a nonseparable system rather than relying on the published SRNN formulation | GFNN · PCR3BP | trajectory prediction error | Helped |
| Approximate the generating function with a neural network so the learned map remains exactly symplectic | GFNN · Integrable Hamiltonian dynamics | long-time prediction error growth | Helped |
| Use GFNN rather than VFNN | Hénon-Heiles · Hénon-Heiles, chaotic sea | statistical pattern accuracy | Helped |
Closest papers by meaning
- Neural Symplectic Form: Learning Hamiltonian Equations on General Coordinate Systems (NeurIPS 2021 · similarity 0.90)
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- Symplectic Spectrum Gaussian Processes: Learning Hamiltonians from Noisy and Sparse Data (NeurIPS 2022 · similarity 0.89)
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- Learned Lagrangian Models of PDEs via Euler–Lagrange Residual Minimization (NeurIPS 2026 · similarity 0.86)
- Learning invariant representations of time-homogeneous stochastic dynamical systems (ICLR 2024 · similarity 0.86)
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