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.

翻译：本文针对一类度量图（称为具有欧几里得边的图）上连续索引的高斯随机场模拟问题展开研究，这类图相较于线性网络更具普适性和灵活性。我们提出了三种通用算法，可重构具有特定度量（即电阻度量，该度量源自近期文献）相关函数的大范围随机场。这些算法应用于由街道网络构成的合成案例研究。实验证明，所提算法快速且精准：既能重现目标相关函数，又能生成有限维分布近似高斯的随机场。