Learn Only Where You Can't Compute: Structured Corrections to Gaussian Process Posteriors
Physics-informed Gaussian processes (GPs) provide a principled framework for scientific inference by expressing uncertainty over empirical measurements, boundary conditions, and governing equations. However, they struggle to scale to larger datasets and nonlinear information. Conversely, diffusion models excel at learning complex distributions over functions from massive datasets, but struggle in scientific contexts where training data are scarce and physical or observational information must be incorporated. We propose a structured posterior-correction framework that combines a tractable Gaussian reference with data-driven corrections via generative learning. After a mean correction and ...
| Authors | Tobias Weber, Carla Sagebiel, Philipp Hennig |
|---|---|
| Primary category | cs.LG |
| Published | 15 October 2026 |
| Last updated at source | 15 October 2026 |
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