Numerical methods for the discretization of random fields by means of the Karhunen–Loève expansion

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Learning soil parameters and updating geotechnical reliability estimates under spatial variability – theory and application to shallow foundations (2017, methodology): “A method that is optimal in terms of the average mean-square error in the discretisation, and hence can lead to efficient RF representation with small number of RVs, is the Karhunen–Loève expansion (e.g. Ghanem and Spanos 1991; Betz, Papaioannou, and Straub 2014).”
Non-Denoising Forward-Time Diffusions (2023, background): “Alternative scalable approaches abound, from Gaussian Markov Random Fields (Rue & Tjelmeland, 2002; Rue, 2001) to Karhunen–Loève expansions (Betz et al., 2014).”
Simulator-free solution of high-dimensional stochastic elliptic partial differential equations using deep neural networks (2019, methodology): “We perform a preliminary dimensionality reduction on the stochastic process A(x, ω) using a truncated KLE [60] and we retain dξ = 129 terms corresponding to 95% energy of the conductivity field.”