Research map / Probabilistic and scientific modeling / Dynamical systems
Symplectic Spectrum Gaussian Processes: Learning Hamiltonians from Noisy and Sparse Data
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use symplectic RFF Hamiltonian GP instead of D-SymODEN for friction coefficient estimation | SSGP · Pendulum | MSE of friction coefficient (x10^3): 1.010 -> 0.519 | Helped |
| use SSGP instead of D-SymODEN for friction coefficient estimation | SSGP · Duffing oscillator | MSE of friction coefficient (x10^3): 0.630 -> 0.506 | Helped |
| use SSGP instead of D-HNN for friction coefficient estimation | SSGP · Pendulum | MSE of friction coefficient (x10^3): 2.486 -> 0.519 | Helped |
| train with finite-difference derivatives (HNN, D-HNN, SympGPR) instead of ODE-solver trajectory learning | Hamiltonian models · noisy sparse trajectories, 5 Hz | MSE of predicted trajectories | Hurt |
| remove Hamiltonian prior (NODE, standard RFF GP) versus SSGP (ablation) | SSGP · Task 1 and Task 2 | MSE of predicted trajectories | Helped |
| standard RFF GP and NODE on dissipative data for unseen friction prediction | NODE and RFF · Task 2 conservative prediction | MSE of predicted trajectories | Mixed |
| increase number of training trajectories (10 to 50) | All models · Pendulum and Duffing, 5 Hz | MSE of predicted trajectories | Helped |
| compare SSGP with SymODEN and D-SymODEN when trajectories are few | SSGP · sparse settings, 5 Hz | MSE of predicted trajectories | Helped |
| evaluate beyond training horizon (10 to 15 s) versus baselines | SSGP · Pendulum cumulative trajectory and energy error | cumulative error | Helped |
| increase number of spectral points M (ablation) | SSGP prior approximation · gram matrix comparison | approximation quality of kernel | Helped |
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