MST-Direct: Matching via Sinkhorn Transport for Multivariate Geostatistical Simulation with Complex Non-Linear Dependencies
This addresses the challenge for geostatistical modeling where traditional methods like Gaussian Copula fail to preserve complex joint distribution patterns, offering a more accurate simulation approach.
The paper tackled the problem of multivariate geostatistical simulation with complex non-linear dependencies, such as bimodal distributions and heteroscedastic relationships, by proposing MST-Direct, a novel algorithm based on Optimal Transport theory that uses the Sinkhorn algorithm to directly match multivariate distributions while preserving spatial correlation structures.
Multivariate geostatistical simulation requires the faithful reproduction of complex non-linear dependencies among geological variables, including bimodal distributions, step functions, and heteroscedastic relationships. Traditional methods such as the Gaussian Copula and LU Decomposition assume linear correlation structures and often fail to preserve these complex joint distribution patterns. We propose MST-Direct (Matching via Sinkhorn Transport), a novel algorithm based on Optimal Transport theory that uses the Sinkhorn algorithm to directly match multivariate distributions while preserving spatial correlation structures. The method processes all variables simultaneously as a single multidimensional vector, enabling relational matching across the full joint space rather than relying on pairwise linear dependencies.