arXiv Machine Learning October 9, 2026 By Mads Greisen H{\o}jlund, August Smart Lykke-M{\o}ller, Henry Moss, Ove Christiansen

Don't Get Your Kroneckers in a Twist: Gaussian Processes on High-Dimensional Incomplete Grids

Read the original on arXiv Machine Learning →

The paper introduces CUTS-GPR, a method for exact Gaussian Process Regression (GPR) in high-dimensional settings. It achieves near-linear scaling in the number of training points and low-order polynomial scaling in dimensionality by using an additive kernel on an incomplete grid, enabling efficient kernel matrix-vector products. Benchmarks demonstrate scalability to billions of data points and thousands of dimensions, with full GPR runs on up to 4.5 million points in 500 dimensions and practical application to ten high-dimensional potential energy surfaces completed in hours.

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