A hybrid Nyström-Karhunen-Loève expansion and orthogonal residual spectral sampling framework for non-Gaussian 3D random field simulation

Efficient simulation of large-scale non-Gaussian three-dimensional random fields remains challenging. Truncated Karhunen-Loève expansion (KLE) captures the dominant correlation structure but often leaves local variance deficits and unresolved complementary fluctuations, whereas direct decomposition of the full covariance matrix becomes prohibitively expensive on fine grids. This study develops a hybrid random field representation framework coupling Nyström-KLE with orthogonal residual spectral sampling in the latent Gaussian space under the Nataf model. A Sobol-sampled Nyström-KLE discretization is used to construct the retained low-rank component and define the retained Nyström-KLE subspace. A sampled spectral field is incorporated into the same latent Gaussian synthesis. Because it generally contains a component in the retained Nyström-KLE subspace, direct superposition would alter the prescribed retained modal coefficients and cause double counting. The sampled spectral field is therefore projected onto the retained subspace, and its duplicated retained subspace contribution is removed to form an orthogonally corrected spectral residual. The assembled latent Gaussian field is finally mapped to the target non-Gaussian field by pointwise marginal transformation. Under the stationary benchmark defined by an exponential correlation model and a Weibull marginal distribution, the proposed framework yields a Kolmogorov-Smirnov statistic of 0.0044. It markedly improves local variance recovery and reduces the directional correlation root mean square errors from 0.0599, 0.0432, and 0.0242 to 0.0117, 0.0136, and 0.0163 in the x-, y-, and z-directions, respectively. Additional tests with alternative correlation functions, marginal distributions, and a stronger non-Gaussian case further support the robustness of the framework. The framework also remains computationally feasible on regular grids up to 8 × 10 6 nodes, while the blockwise implementation keeps the memory demand low.