Non-stationary Gaussian random fields on hypersurfaces: Sampling and strong error analysis

TL;DR

This paper introduces a flexible model for non-stationary Gaussian random fields on hypersurfaces, analyzing sampling methods and providing strong error bounds with numerical validation.

Contribution

It develops a novel framework for modeling non-stationary Gaussian fields on hypersurfaces using spectral densities and finite element methods.

Findings

Strong error bounds with explicit convergence rates

Numerical experiments confirm theoretical convergence rates

Effective sampling via Galerkin--Chebyshev approximation

Abstract

A flexible model for non-stationary Gaussian random fields on hypersurfaces is introduced.The class of random fields on curves and surfaces is characterized by an amplitude spectral density of a second order elliptic differential operator.Sampling is done by a Galerkin--Chebyshev approximation based on the surface finite element method and Chebyshev polynomials. Strong error bounds are shown with convergence rates depending on the smoothness of the approximated random field. Numerical experiments that confirm the convergence rates are presented.