On the Correspondence between Gaussian Processes and Geometric Harmonics

2021/10/05 by Felix Dietrich, Dietrich, Felix, Juan M. Bello‐Rivas +3
Computer Science · Physics and Astronomy · #42-08 #42-XX #60G15 #Advanced Multi-Objective Optimization Algorithms #FOS: Computer and information sciences #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks #Optimization and Control (math.OC) #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2110.02296

openalex publication_date 2021/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss the correspondence between Gaussian process regression and Geometric Harmonics, two similar kernel-based methods that are typically used in different contexts. Research communities surrounding the two concepts often pursue different goals. Results from both camps can be successfully combined, providing alternative interpretations of uncertainty in terms of error estimation, or leading towards accelerated Bayesian Optimization due to dimensionality reduction.

Citations

• Taking the Human Out of the Loop: A Review of Bayesian Optimization
• Diffusion maps for embedded manifolds with boundary with applications to PDEs
• Understanding and mitigating gradient pathologies in physics-informed neural networks

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