Computationally Efficient Algorithms for Simulating Isotropic Gaussian Random Fields on Graphs with Euclidean Edges

TL;DR: This work introduces three computationally efficient algorithms for simulating isotropic Gaussian random fields on graphs with Euclidean edges, enabling the reconstruction of various random fields with specific covariance functions and finite-dimensional Gaussian distributions.

Abstract: This work addresses the problem of simulating Gaussian random fields that are continuously indexed over a class of metric graphs, termed graphs with Euclidean edges, being more general and flexible than linear networks. We introduce three general algorithms that allow to reconstruct a wide spectrum of random fields having a covariance function that depends on a specific metric, called resistance metric, and proposed in recent literature. The algorithms are applied to a synthetic case study consisting of a street network. They prove to be fast and accurate in that they reproduce the target covariance function and provide random fields whose finite-dimensional distributions are approximately Gaussian.