Easy representation of multivariate functions with low-dimensional terms via Gaussian process regression kernel design: applications to machine learning of potential energy surfaces and kinetic energy densities from sparse data

TL;DR

This paper introduces a Gaussian process regression kernel design that efficiently represents multivariate functions with low-dimensional components, improving machine learning of potential energy surfaces and kinetic energy densities from sparse data.

Contribution

The authors develop a kernel based on HDMR for GPR, offering a faster, simpler alternative to existing HDMR-GPR methods for modeling multivariate functions.

Findings

Effective in fitting potential energy surfaces from sparse data

Accurate modeling of kinetic energy densities with fewer data points

Simplifies the use of HDMR in Gaussian process regression

Abstract

We show that Gaussian process regression (GPR) allows representing multivariate functions with low-dimensional terms via kernel design. When using a kernel built with HDMR (High-dimensional model representation), one obtains a similar type of representation as the previously proposed HDMR-GPR scheme while being faster and simpler to use. We tested the approach on cases where highly accurate machine learning is required from sparse data by fitting potential energy surfaces and kinetic energy densities.