Gaussian Processes for High-Frequency PDE Solutions
Published on:
8 November 2023
Primary Category:
Machine Learning
Paper Authors:
Shikai Fang,
Madison Cooley,
Da Long,
Shibo Li,
Robert Kirby,
Shandian Zhe
Bullets
Key Details
Models PDE solution spectrum with mixtures to capture frequencies
Derives effective covariance function via Fourier transform
Enables automatic sparsity and frequency estimation
Uses grid structure and Kronecker products for efficiency
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AI generated summary
Gaussian Processes for High-Frequency PDE Solutions
This paper develops a Gaussian process framework to accurately solve partial differential equations containing high-frequency components. It models the power spectrum with mixtures to capture dominant frequencies. The covariance function derived enables automatic sparsity and frequency estimation.
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