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

TL;DR

This paper introduces three efficient algorithms for simulating Gaussian random fields on complex metric graphs with Euclidean edges, enabling accurate and fast reconstruction of fields with covariance based on resistance metrics.

Contribution

The work presents novel algorithms that generalize simulation methods to a broad class of metric graphs, improving flexibility and computational efficiency.

Findings

Algorithms accurately reproduce target covariance functions.

Simulations are computationally fast and scalable.

Finite-dimensional distributions are approximately Gaussian.

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.