🤖 AI Summary
Multivariate geostatistical simulation struggles to accurately represent complex nonlinear dependence structures such as bimodal distributions, stepwise relationships, and heteroscedasticity. This work proposes a novel approach grounded in optimal transport theory, leveraging the Sinkhorn algorithm to directly match high-dimensional joint distributions. By treating all variables holistically and processing them simultaneously, the method achieves end-to-end faithful reconstruction of the full joint distribution while preserving spatial correlations. It overcomes the limitations of conventional assumptions based on linear correlation or Gaussian copulas, marking the first successful reproduction of intricate nonlinear dependencies in multivariate geostatistical simulation. Experimental results demonstrate its significant superiority over existing techniques, including LU decomposition and Gaussian copula-based methods.
📝 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.