Research map / Probabilistic and scientific modeling / Dynamical systems
Nonseparable Symplectic Neural Networks
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use NSSNN instead of the strongest listed baseline | Hamiltonian prediction · Pendulum | prediction error: 3.4\times 10^{-2} -> 2.6\times 10^{-2} | Helped |
| Use NSSNN instead of NeuralODE | Hamiltonian prediction · Lotka-Volterra | prediction error: 2.2\times 10^{-2} -> 2.7\times 10^{-2} | Hurt |
| Use NSSNN instead of NeuralODE | Hamiltonian prediction · Spring | prediction error: 2.1\times 10^{-2} -> 1.6\times 10^{-2} | Helped |
| Use NSSNN instead of HNN | Hamiltonian prediction · Hénon–Heiles | prediction error: 9.4\times 10^{-2} -> 8.4\times 10^{-2} | Helped |
| Use NSSNN instead of HNN | Hamiltonian prediction · Tao's example | prediction error: 2.6\times 10^{-2} -> 2.2\times 10^{-2} | Helped |
| Use NSSNN instead of HNN | Hamiltonian prediction · Schrödinger | prediction error: 5.9\times 10^{-2} -> 5.7\times 10^{-2} | Helped |
| Use NSSNN instead of HNN | Hamiltonian prediction · Two Vortices | prediction error: 7.7\times 10^{-3} -> 3.4\times 10^{-3} | Helped |
| Use NSSNN instead of HNN | Hamiltonian prediction · Four vortices | Hamiltonian deviation: 1.4\times10^{-2} -> 3.4\times10^{-3} | Helped |
| Use the augmented nonseparable symplectic integrator for prediction (ablation) | IHNN · Spring, long-term prediction | prediction accuracy | Helped |
| Train with L1 rather than MSE (ablation) | NSSNN · Noisy training data | validation loss | Helped |
| Train with L1 rather than MSE (ablation) | NSSNN · Clean training data | validation loss | Mixed |
| Increase the integrator step size (ablation) | NSSNN · Longer training time span | validation loss | Hurt |
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