Galerkin-Chebyshev approximation of Gaussian random fields on compact Riemannian manifolds
Preprint, 2021

A new numerical approximation method for a class of Gaussian random fields on compact Riemannian manifolds is introduced. This class of random fields is characterized by the Laplace-Beltrami operator on the manifold. A Galerkin approximation is combined with a polynomial approximation using Chebyshev series. This so-called Galerkin-Chebyshev approximation scheme yields efficient and generic sampling algorithms for Gaussian random fields on manifolds. Strong and weak orders of convergence for the Galerkin approximation and strong convergence orders for the Galerkin-Chebyshev approximation are shown and confirmed through numerical experiments.

Galerkin approximation

Weak convergence

Laplace-Beltrami operator

Whittle-Matérn fields

Chebyshev polynomials

Compact Riemannian manifolds

Strong convergence

Gaussian random fields

Author

Annika Lang

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

Mike Pereira

Chalmers, Electrical Engineering, Systems and control, Automatic Control

Efficient approximation methods for random fields on manifolds

Swedish Research Council (VR) (2020-04170), 2021-01-01 -- 2024-12-31.

Stochastic Continuous-Depth Neural Networks

Chalmers AI Research Centre (CHAIR), 2020-08-15 -- .

STOchastic Traffic NEtworks (STONE)

Chalmers AI Research Centre (CHAIR), -- .

Chalmers, 2020-02-01 -- 2022-01-31.

Areas of Advance

Transport

Subject Categories

Computational Mathematics

Probability Theory and Statistics

Mathematical Analysis

Roots

Basic sciences

Related datasets

arXiv:2107.02667 [math.NA] [dataset]

URI: https://arxiv.org/abs/2107.02667

More information

Created

8/11/2021