Learn Only Where You Can't Compute: Structured Corrections to Gaussian Process Posteriors

Key points

• Physics-informed Gaussian processes (GPs) provide a principled framework for scientific inference by expressing uncertainty over empirical measurements, boundary conditions, and governing equations.1
• After a mean correction and covariance calibration, a diffusion model learns a targeted correction in a low-dimensional subspace selected to capture discrepancies from the reference, while the complement retains its Gaussian law.1
• Across three scientific inference tasks, these corrections recover hidden modes, improve sample structure, and reduce prediction error relative to the Gaussian reference.1
• Comparisons with full-field generative models reveal task-dependent benefits and tradeoffs between predictive accuracy and computational cost.1

Sources (1)

• [1]Learn Only Where You Can't Compute: Structured Corrections to Gaussian Process Posteriors
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 15, 02:31 PM

  We propose a structured posterior-correction framework that combines a tractable Gaussian reference with data-driven corrections via generative learning.

  Physics-informed Gaussian processes (GPs) provide a principled framework for scientific inference by expressing uncertainty over empirical measurements, boundary conditions, and governing equations.

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