MST-Direct：基于Sinkhorn传输的多变量地理统计模拟匹配
MST-Direct: Matching via Sinkhorn Transport for Multivariate Geostatistical Simulation with Complex Non-Linear Dependencies
AI总结：
本文提出MST-Direct算法，利用Sinkhorn算法直接匹配多变量分布，保留空间相关结构，解决传统方法无法处理复杂非线性依赖的问题。
摘要：
多变量地理统计模拟需要忠实再现地质变量间的复杂非线性依赖关系，包括双峰分布、阶梯函数和异方差关系。传统方法如高斯Copula和LU分解假设线性相关结构，常无法保持这些复杂联合分布模式。我们提出MST-Direct（基于Sinkhorn传输的匹配），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，同时保留空间相关结构。该方法将所有变量同时作为单个多维向量处理，实现整个联合空间内的关系匹配，而非依赖成对线性依赖。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
