Wasserstein空间最大最小距离设计的构造及其近似算法  

Construction of Maximin Distance Designs in Wasserstein Spaces and an Approximate Algorithm

作　　者：牟唯嫣 靳旭玲 熊世峰[2] MU Weiyan;JIN Xuling;XIONG Shifeng(School of Science,Beijing University of Civil Engineering and Architecture,Beijng 102616;Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190)

机构地区：[1]北京建筑大学理学院,北京102616 [2]中国科学院数学与系统科学研究院,北京100190

出　　处：《系统科学与数学》2023年第9期2364-2372,共9页Journal of Systems Science and Mathematical Sciences

基　　金：国家重点研发计划(2021YFA1000300,2021YFA1000301,2021YFA1000303);国家自然科学基金(12171462)资助项目。

摘　　要：文章研究了Wasserstein空间中空间填充设计的构造问题.文章将Wasserstein空间通过参数化进行有限维逼近,将最大化设计的最小Wasserstein距离这一优化问题转化为近似的有限维问题,再提出了一个坐标下降算法对其求解.数值算例和在地铁仿真中的应用表明所提出的算法能得到具有优良空间填充性质的设计方案.Computer experiments with distributional inputs can be applied to study complex systems that involve a great deal of uncertainty.A Wasserstein space is suitable as the domain of such distributional inputs.However,there is little work on construction of space-filling designs in a Wasserstein space in the literature.This paper studies the problem of constructing maximin Wasserstein distance designs in a Wasserstein space.This paper first uses parameterization to approximate the Wasserstein space.Then the infinity-dimensional Wasserstein space can be approximated by a finite-dimensional space.Consequently,the optimization problem of maximizing the minimum Wasserstein distance criterion is replaced by a finite-dimensional problem.A coordinate descent algorithm is proposed to solve it.In this algorithm,we only optimize one row in the design matrix at each step,and this reduces computational cost significantly.Numerical examples and a real application to a metro simulation indicate that the proposed algorithm can yield designs with good space-filling properties.

关 键 词：坐标下降算法 空间填充设计 随机计算机试验 Wasserstein距离 

分 类 号：O212.6[理学—概率论与数理统计]