Bdrygp: A Boundary-Integrated Gaussian Process Model For Computer Code Emulation
summary
BdryGP integrates Dirichlet boundary information directly into Gaussian process emulators, giving closed‑form Matérn‑based kernels that force zero variance on specified faces and improve prediction across the domain. The model proves faster convergence rates and quicker posterior contraction than standard GPs, and uses sparse grid designs so posterior updates scale efficiently (authors report sparse grid linear‑time posterior computation). Numerical tests and a rocket injector case with expensive runs (one LES run ~6‑week runs or injector ~14 days) show much tighter uncertainty and better accuracy.
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chapters (19)
- 0:00Intro
- 2:16Science-guided statistical learning
- 3:44Computer experiments
- 4:32Rocket injector design
- 5:56Rocket engine design
- 9:07Gaussian processes
- 13:00A true story
- 14:41Boundaries as prior information
- 19:16Boundary assumptions
- 21:241-0 BdryMatérn covariance
- 23:44Product BdryMatém covariance
- 24:27Putting everything together
- 25:28Are we done?
- 26:07Full grid design
- 29:55Prediction rates
- 30:51Scalability via sparse grids
- 32:00Numerical examples
- 34:55Conclusion
- 36:23Questions
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