Research map / Probabilistic and scientific modeling / Differential equations and PDEs
Probabilistic ODE Solutions in Millions of Dimensions
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Assume independent dimensions (diagonal diffusion) so each dimension is updated separately | ODE filter single step · Lorenz96 single-step runtime | per-step runtime scaling: O(d) instead of O(d^3) | Helped |
| Exploit Kronecker structure (scalar calibrated diffusion) in the EK0 (ablation) | EK0 ODE filter · Lorenz96 single-step runtime | per-step runtime: Kronecker EK0 significantly faster than diagonal versions | Helped |
| Diagonal Jacobian approximation (diagonal EK1) instead of full EK1 (ablation) | EK1 stiffness stability on Van der Pol · Van der Pol stiffness sweep | number of steps taken | Mixed |
| Use diagonal EK1 instead of EK0 (diagonal Jacobian information) (ablation) | ODE filter stability · Van der Pol stiffness sweep | number of steps taken | Helped |
| Use the full Jacobian and independent-dimension prior on the Pleiades problem | Fast ODE filter implementation · Pleiades (28 dims) runtime per RMSE | runtime per RMSE: 100 times faster than reference implementations | Helped |
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