Modeling Nonstationary Non-Gaussian Random Fields: A D-Vine Copula Approach

Random field modeling and simulation is crucial in engineering applications. Traditional approaches often rely on Gaussian assumptions and covariance-based structures, which can fail to capture complex non-Gaussian dependencies. By leveraging copula theory, the D-vine copula model decouples marginal distributions from the dependence structure, enabling flexible and accurate representation of both components. Despite its potential, a systematic investigation of the D-vine copula model for nonstationary, non-Gaussian random fields is still lacking, limiting its broader application. In addition, the high dimensionality of the discretized random field leads to extremely large D-vine structures, posing significant computational challenges for both model construction and simulation. This study provides a comprehensive framework for the modeling and simulation of random fields using D-vine copulae, including an improved tree representation of the model and the development of specific algorithms. A truncation scheme is further proposed to reduce computational cost while preserving sufficient accuracy, thereby enabling the practical use of D-vine copulae for nonstationary, non-Gaussian random fields. Numerical examples, involving random fields with Gaussian and non-Gaussian dependencies and marginals, are presented to demonstrate the effectiveness of the complete and truncated D-vine copula models. The results show that the proposed truncation strategy achieves substantial efficiency gains without compromising accuracy. The proposed framework provides a promising foundation for future research, with remaining challenges including the selection of appropriate pairwise copula families and the development of efficient numerical techniques for truncation error estimation.