| --- |
| license: apache-2.0 |
| tags: |
| - scientific-machine-learning |
| - hamiltonian-neural-network |
| - differentiable-physics |
| - neural-ode |
| - gradio |
| --- |
| |
| # Hamiltonian Pocket |
|
|
| Hamiltonian Pocket learns pendulum dynamics from state/derivative observations. |
| The structured model predicts one scalar Hamiltonian and obtains time derivatives |
| through the symplectic gradient. A parameter-matched MLP directly predicts the two |
| derivatives. Both train on the same samples and use the same RK4 solver at test time. |
|
|
| The benchmark measures local derivative error, long-horizon state error, and drift |
| in the true physical energy. It tests whether encoding conservative mechanics in the |
| model helps trajectories remain physically plausible. |
|
|
| ## Verified results |
|
|
| Both models trained for 3,000 steps on 20,000 states. Long-horizon evaluation used |
| 128 new initial conditions, 400 RK4 steps, and `dt=0.05`. |
|
|
| | Metric | Hamiltonian network | Black-box vector field | |
| | --- | ---: | ---: | |
| | Parameters | 4,417 | 4,482 | |
| | Held-out derivative MSE | 4.84e-6 | 1.13e-5 | |
| | Full-trajectory MSE | 49.00 | 119.89 | |
| | Final-state MSE | 201.84 | 439.03 | |
| | Final absolute true-energy drift | 2.95 | 343.11 | |
|
|
| The Hamiltonian inductive bias reduced final energy drift by about 116 times. It |
| did not eliminate drift in the true physical energy: the learned scalar Hamiltonian |
| is an approximation, and small derivative errors accumulate over 20 simulated |
| seconds. |
|
|
| ## Reproduce |
|
|
| ```powershell |
| uv run python projects/hamiltonian-pocket/train.py |
| ``` |
|
|
