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Sparse Symplectically Integrated Neural Networks
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use sparse SSINN parameterization instead of an SRNN | Coupled-oscillator prediction · Coupled oscillators, clean data | Prediction error: 3 \cdot 10^{-3} -> 2 \cdot 10^{-8} | Helped |
| Use a third-degree polynomial basis rather than a higher-degree SSINN basis (ablation) | SSINN · Coupled oscillators, noisy data | Position L1-error: 3.8 \cdot 10^{-3} -> 6.6 \cdot 10^{-4} | Helped |
| Use a third-degree polynomial basis rather than a higher-degree SSINN basis (ablation) | SSINN · Coupled oscillators, noisy data | Momentum L1-error: 3.1 \cdot 10^{-3} -> 5.6 \cdot 10^{-4} | Helped |
| Replace fourth-order symplectic integration with RK4 (ablation) | Sparse network on Hénon-Heiles · Hénon-Heiles | L1-error: 4 orders of magnitude greater | Hurt |
| Use a polynomial-and-trigonometric function space instead of a restricted true-equation basis (ablation) | SSINN pendulum model · Pendulum | Prediction error: 5.8 \cdot 10^{-6} -> 10^{-4} precision | Hurt |
| Omit trigonometric terms and use fifth-degree polynomial terms (ablation) | SSINN pendulum model · Pendulum | Prediction error: 5.8 \cdot 10^{-6} -> 7\cdot 10^{-5} | Hurt |
| Train on only 200 noisy state transitions | SSINN · Coupled oscillators | Governing-equation recovery: 200 | Helped |
| Use SSINN rather than SRNN on noisy coupled-oscillator data | Coupled-oscillator prediction · Coupled oscillators, noisy data | Position L1-error: 1.5 \cdot 10^{-1} -> 6.6 \cdot 10^{-4} | Helped |
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