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

• URL: http://arxiv.org/abs/2605.08036v1
• Date: Fri, 08 May 2026 17:24:22 GMT
• Title: Don't Get Your Kroneckers in a Twist: Gaussian Processes on High-Dimensional Incomplete Grids
• Abstract summary: We introduce CUTS-GPR, a new method for performing numerically exact process regression (GPR) in high-dimensional settings.<n>The key component of CUTS-GPR is an extremely fast kernel matrix-vector product.<n>We demonstrate that our CUTS-GPR enables modeling of high-dimensional potential energy surfaces.
• Score: 0.5833117322405447
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We introduce CUTS-GPR, a new method for performing numerically exact Gaussian process regression (GPR) in high-dimensional settings. The key component of CUTS-GPR is an extremely fast kernel matrix-vector product, which exhibits near-linear or even linear scaling with the amount of training data, $N$, and low-order polynomial scaling with dimensionality, $D$. This is obtained by combining an additive kernel with an incomplete grid and exploiting the resulting structure of the kernel matrix. We demonstrate the scalability of the matrix-vector product by running benchmarks with billions of data points and thousands of dimensions. Full GPR calculations, including hyperparameter optimization, are completed in a matter of hours for $N = 447 265$ and $D = 24$. We demonstrate that our CUTS-GPR enables Bayesian modeling of high-dimensional potential energy surfaces - a longstanding challenge in computational chemistry.

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