用最优传输直接匹配复杂地质变量分布，保持空间相关性。
MST-Direct: Matching via Sinkhorn Transport for Multivariate Geostatistical Simulation with Complex Non-Linear Dependencies
- 基于Sinkhorn算法的联合分布直接匹配，避免线性假设
- 同时处理多变量向量，捕捉非线性依赖关系
- 适合含双峰、异方差等复杂结构的地质模拟
多变量地质统计模拟需准确再现地质变量间的复杂非线性依赖关系，包括双峰分布、阶跃函数及异方差关系。传统方法如高斯互换和LU分解依赖线性相关结构，常无法保留这些复杂的联合分布模式。我们提出MST-Direct（通过Sinkhorn传输进行匹配），一种基于最优传输理论的新算法，利用Sinkhorn算法直接匹配多变量分布，同时保持空间相关结构。该方法将所有变量作为单一多维向量处理，实现全联合空间内的关系匹配，而非依赖成对线性依赖关系。
原文摘要 · Abstract (English)
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.
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