MST-Direct: Matching via Sinkhorn Transport for Multivariate Geostatistical Simulation with Complex Non-Linear Dependencies

TL;DR

MST-Direct employs Sinkhorn Transport to accurately match complex multivariate distributions in geostatistical simulations, effectively capturing non-linear dependencies and preserving spatial correlations.

Contribution

This paper introduces MST-Direct, a novel optimal transport-based algorithm that directly matches multivariate distributions in geostatistics, overcoming limitations of linear assumptions.

Findings

Successfully reproduces complex non-linear dependencies

Preserves spatial correlation structures in simulations

Outperforms traditional linear methods in accuracy

Abstract

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.