Research map / Probabilistic and scientific modeling / Dynamical systems
Identifying Physical Law of Hamiltonian Systems via Meta-Learning
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use HANIL instead of the strongest baseline | New Hamiltonian systems · Spring-Mass, point dynamics and trajectories | MSE: 8.2$\pm$13.3 -> 0.02$\pm$0.01; 4.9$\pm$6.6 -> 0.01$\pm$0.006; 11.9$\pm$14.1 -> 0.4$\pm$0.4; 6.6$\pm$10.0 -> 0.1$\pm$0.07 | Helped |
| Use HANIL instead of Naive NN + ANIL | New Hamiltonian systems · Pendulum, point dynamics and trajectories | MSE: 2.3$\pm$1.8 -> 0.02$\pm$0.04; 2.0$\pm$1.4 -> 0.003$\pm$0.001; 3.3$\pm$2.4 -> 0.6$\pm$1.2; 2.8$\pm$1.8 -> 0.04$\pm$0.02 | Helped |
| Use HANIL instead of Naive NN + ANIL | New Hamiltonian systems · Kepler, point dynamics and trajectories | MSE: 1.1$\pm$0.9 -> 0.33$\pm$0.19; 0.9$\pm$0.6 -> 0.33$\pm$0.18; 2.4$\pm$3.3 -> 0.33$\pm$0.19; 1.2$\pm$0.9 -> 0.33$\pm$0.18 | Helped |
| Use meta-learning rather than training HNN from scratch or pretraining across systems (ablation) | HNN for new pendulum systems · Pendulum, 50 point dynamics | MSE | Helped |
| Separate shared representation and task-specific parameters during adaptation (ablation) | HAMAML · Pendulum, 50 point dynamics | MSE | Helped |
| Update only the last layer during inner-loop adaptation (ablation) | HANIL · Pendulum, 50 point dynamics | MSE | Helped |
| Increase meta-training task count (ablation) | Meta-trained learners · Pendulum, 50 point dynamics | MSE | Helped |
| Use point dynamics rather than trajectories with the same number of samples | Hamiltonian learners · All physical systems | MSE | Helped |
Closest papers by meaning
- Towards Cross Domain Generalization of Hamiltonian Representation via Meta Learning (ICLR 2024 · similarity 0.91)
- Hamiltonian Score Matching and Generative Flows (NeurIPS 2024 · similarity 0.88)
- Physics-Informed Regularization for Domain-Agnostic Dynamical System Modeling (NeurIPS 2024 · similarity 0.86)
- Discovering Physics Laws of Dynamical Systems via Invariant Function Learning (ICML 2025 · similarity 0.86)
- Hamiltonian Neural PDE Solvers through Functional Approximation (NeurIPS 2025 · similarity 0.86)
- Noether's Razor: Learning Conserved Quantities (NeurIPS 2024 · similarity 0.85)
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