Numerical modeling is essential for comprehending intricate physical phenomena in different domains. To handle complexity, sensitivity analysis, particularly screening, is crucial for identifying influential input parameters. Kernel-based methods, such as the Hilbert Schmidt Independence Criterion (HSIC), are valuable for analyzing dependencies between inputs and outputs. Moreover, due to the computational expense of such models, metamodels (or surrogate models) are often unavoidable. Implementing metamodels and HSIC requires data from the original model, which leads to the need for space-filling designs. While existing methods like Latin Hypercube Sampling (LHS) are effective for independent variables, incorporating dependence is challenging. This paper introduces a novel LHS variant, Quantization-based LHS, which leverages Voronoi vector quantization to address correlated inputs. The method ensures comprehensive coverage of stratified variables, enhancing distribution across marginals. The paper outlines expectation estimators based on Quantization-based LHS in various dependency settings, demonstrating their unbiasedness. The method is applied on several models of growing complexities, first on simple examples to illustrate the theory, then on more complex environmental hydrological models, when the dependence is known or not, and with more and more interactive processes and factors. The last application is on the digital twin of a French vineyard catchment (Beaujolais region) to design a vegetative filter strip and reduce water, sediment and pesticide transfers from the fields to the river. Quantization-based LHS is used to compute HSIC measures and independence tests, demonstrating its usefulness, especially in the context of complex models.

翻译：数值建模对于理解不同领域中复杂的物理现象至关重要。为应对复杂性，敏感性分析（特别是筛选分析）在识别关键输入参数方面具有关键作用。基于核的方法（如希尔伯特-施密特独立性准则，HSIC）能够有效分析输入与输出之间的依赖关系。此外，由于此类模型计算成本高昂，元模型（或代理模型）往往不可或缺。实施元模型和HSIC需要原始模型数据，因此需采用空间填充设计。现有方法如拉丁超立方抽样在处理独立变量时效果显著，但难以融入变量间的相关性。本文提出一种新型拉丁超立方抽样变体——基于量化的拉丁超立方抽样，通过利用沃罗诺伊向量量化技术处理相关输入变量。该方法确保对分层变量的全面覆盖，增强边际分布的采样效能。论文针对不同依赖场景构建了基于量化拉丁超立方抽样的期望估计量，并证明了其无偏性。该方法被应用于复杂度递增的多个模型：首先通过简单示例验证理论，随后应用于更复杂的环境水文模型（涵盖已知与未知依赖关系的情形），并逐步引入更多交互过程与因子。最终应用涉及法国博若莱地区某葡萄园流域的数字孪生模型，旨在设计植被过滤带以减少农田向河流的水体、沉积物和农药输移。采用基于量化的拉丁超立方抽样计算HSIC测度并执行独立性检验，证明了该方法在复杂模型中的实用价值。