标题： LHS中的LHS：模拟设计中拉丁超立方抽样的一种新扩展策略 显示英文标题

标题： LHS in LHS: A new expansion strategy for Latin hypercube sampling in simulation design

摘要： 拉丁超立方采样（LHS）是模拟设计中的一个重要工具，广泛应用于高维和计算成本高昂的问题中。 LHS允许各种优化策略，最著名的是确保空间填充特性。 然而，LHS是一个单阶段算法，需要事先知道目标样本数量。 在本工作中，我们提出LHS in LHS，这是一种新的LHS扩展算法，能够在不破坏其特性的前提下，向现有的LHS分布集添加新样本。 简而言之，该算法识别远离初始集的参数空间区域，在这些区域中绘制一个新的LHS，然后将其与原始样本合并。 作为副产品，我们引入了一个新的度量标准，即LHS度，用于量化给定设计与LHS分布的偏离程度。 我们的公开实现通过Python包expandLHS进行分发。 显示英文摘要

摘要： Latin Hypercube Sampling (LHS) is a prominent tool in simulation design, with a variety of applications in high-dimensional and computationally expensive problems. LHS allows for various optimization strategies, most notably to ensure space-filling properties. However, LHS is a single-stage algorithm that requires a priori knowledge of the targeted sample size. In this work, we present LHS in LHS, a new expansion algorithm for LHS that enables the addition of new samples to an existing LHS-distributed set while (approximately) preserving its properties. In summary, the algorithm identifies regions of the parameter space that are far from the initial set, draws a new LHS within those regions, and then merges it with the original samples. As a by-product, we introduce a new metric, the LHS degree, which quantifies the deviation of a given design from an LHS distribution. Our public implementation is distributed via the Python package expandLHS.