Research map / Probabilistic and scientific modeling / Differential equations and PDEs
GOODE: A Gaussian Off-The-Shelf Ordinary Differential Equation Solver
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use GP-based quasilinearization (iterated GP regression) to solve nonlinear BVPs | GOODE · Mazzia BVP test set (33 problems) | relative error | No clear effect |
| Use equidistant mesh with small N instead of adaptive mesh | GOODE · Problem 23 of BVP test set | relative error | Hurt |
| Increase number of mesh points N (ablation) | GOODE with log-likelihood length-scale selection · Problems 1, 2, 20, 21 | relative error | Helped |
| Select length scale by maximizing log marginal likelihood instead of reference-based optimum (ablation) | GOODE · BVP test set | relative error | Hurt |
| Vary initial guess y(0) across runs to obtain multiple solutions | GOODE · Painlevé BVP | number of solutions found: 2 vs 1 for bvp5c | Helped |
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