Hamiltonian Neural Networks
About
Even though neural networks enjoy widespread use, they still struggle to learn the basic laws of physics. How might we endow them with better inductive biases? In this paper, we draw inspiration from Hamiltonian mechanics to train models that learn and respect exact conservation laws in an unsupervised manner. We evaluate our models on problems where conservation of energy is important, including the two-body problem and pixel observations of a pendulum. Our model trains faster and generalizes better than a regular neural network. An interesting side effect is that our model is perfectly reversible in time.
Sam Greydanus, Misko Dzamba, Jason Yosinski• 2019
Related benchmarks
| Task | Dataset | Result | Rank | |
|---|---|---|---|---|
| Rollout Prediction | Pendulum | Rollout MSE1.05 | 12 | |
| Rollout Prediction | Fermi-Pasta-Ulam-Tsingou | Rollout MSE0.0107 | 12 | |
| Rollout Prediction | Double pendulum | Rollout MSE1.6 | 12 | |
| Static 5-Body Dynamics Simulation | Static 5-Body Dynamics (test) | MSE4.826 | 10 | |
| Dynamics Prediction | DNLS homogeneous (N=4) (train) | Training Loss1.21 | 7 | |
| Dynamics Prediction | DNLS with heterogeneous node dynamics (test) | Test Loss1.13 | 7 | |
| Learning-adequacy diagnostics | Periodic 2D waves (held-out val) | VF cosine9.999 | 7 | |
| Dynamics Prediction | DNLS homogeneous N=4 (test) | Test loss1.34 | 7 | |
| Dynamics Prediction | DNLS with heterogeneous node dynamics (train) | Train Loss1.93 | 7 | |
| Mesh-based physics simulation | Analytic Mesh Physics Frequency shift | TSMSE1.54 | 7 |
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