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 | |
| Hamiltonian Dynamics Modeling | Double pendulum | Relative L2 Error0.0036 | 5 | |
| State Prediction | nonlinear spring simulations (test) | RMSE0.13 | 5 | |
| State Prediction | 2D pendulum simulations (test) | RMSE0.1 | 5 | |
| Chaotic system approximation | Hénon-Heiles | Relative L2 Error6.68e-4 | 5 | |
| State Prediction | mass-spring simulations (test) | RMSE0.19 | 5 | |
| Hamiltonian approximation | Single pendulum Domain [-2π, 2π] × [-1, 1] | Relative L2 Error0.0022 | 4 |
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