Vector-Valued Gaussian Processes for Approximating Divergence- or Rotation-free Vector Fields

TL;DR

This paper develops a theoretical framework for vector-valued Gaussian processes tailored to approximate divergence- or rotation-free vector fields, providing error estimates and linking to multivariate approximation theory.

Contribution

It introduces a novel Gaussian process model for divergence- or rotation-free vector fields and derives associated error bounds, bridging stochastic processes and approximation theory.

Findings

Established the theory for vector-valued Gaussian processes in this context.

Linked Gaussian process approximation to multivariate approximation theory.

Provided error estimates for the predictive mean in different scenarios.

Abstract

In this paper, we discuss vector-valued Gaussian processes for the approximation of divergence- or rotation-free functions. We establish the theory for such Gaussian processes, then link the theory to multivariate approximation theory, and finally give error estimates for the predictive mean in various situations.