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

Alfredo Alegría

doi:10.1080/10618600.2025.2574535

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

2025-12-01

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DOI：10.1080/10618600.2025.2574535

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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.

Keywords:

Dilution method

Linear network

Metric graph

Resistance metric

Spectral method

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

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