Research map / Probabilistic and scientific modeling / Differential equations and PDEs
Fast Parameter Inference in Nonlinear Dynamical Systems using Iterative Gradient Matching
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add third regularisation step RKG3 over RKG2 (ablation) | gradient matching · Lotka-Volterra sigma=0.25 | parameter RMSE x10^-2: 6.1 -> 4.6 | Helped |
| add third step RKG3 over RKG2 (ablation) | gradient matching · Lotka-Volterra sigma=0.4 | parameter RMSE x10^-2: 10.3 -> 5.4 | Helped |
| RKG3 versus GON | RKG3 · Lotka-Volterra sigma=0.4 | parameter RMSE x10^-2: 7.9 -> 5.4 | Helped |
| RKG3 versus RKG2 (ablation) | RKG3 · protein pathway sigma=0.01 | function RMSE x10^-2: 22.7 -> 5.2 | Helped |
| RKG3 versus GON | RKG3 · protein pathway sigma=0.052 | function RMSE x10^-2: 37 -> 11 | Helped |
| iterative acceleration versus direct minimisation | RKG3 optimisation · Lotka-Volterra eq. (20) | CPU time per iteration: 599.8s -> 6.7s | Helped |
| RKG3 versus GON in compute cost | RKG3 · Lotka-Volterra eq. (20) | CPU time: 4.2s -> 6.7s | Hurt |
| RKG3 vs GON at higher noise on alpha | RKG3 · Lotka-Volterra sigma=0.4 | p-value: 5e-1 | No clear effect |
| RKG3 vs GON/RKG2 on k5/k6 | RKG3 · protein pathway | p-value: 2.1e-1 | No clear effect |
| overall significance of RKG3 improvement | RKG3 · both systems | paired t-tests: 69% | Helped |
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