Physical phenomena are commonly modeled by numerical simulators. Such codes can take as input a high number of uncertain parameters and it is important to identify their influences on the outputs via a global sensitivity analysis (GSA). However, these codes can be time consuming, which prevents a GSA based on the classical Sobol' indices, requiring too many code simulations. To address this limitation, this paper focuses on the Hilbert–Schmidt independence criterion (HSIC) and proposes new goal-oriented algorithms to optimize the permuted HSIC-based independence tests for screening and ranking purposes. Built upon a sample of inputs/outputs of the studied simulator, the HSIC-based tests relies on the estimation of a p-value under independence hypothesis. These p-values can be estimated by a permutation method whatever the sample size, but a reliable estimation based on a large number of permutations can be prohibitive in practice. To overcome this, several strategies are proposed to greedy estimate the p-value, according to the final goal of GSA. Three sequential permuted tests are thus proposed: screening oriented, ranking oriented, and ranking-screening oriented. These algorithms are tested and compared on analytical examples, before being applied on a thermalhydraulic use case simulating an accidental scenario on a nuclear pressurized water reactor. Their efficiency and time saving are clearly demonstrated. Moreover, a convergence study, made computationally tractable by the optimized algorithms, is carried out to assess the robustness of the results on the use case.

中文翻译：

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优化的基于 HSIC 的灵敏度分析测试：在核反应堆事故场景的热水力模拟中的应用

物理现象通常由数值模拟器建模。此类代码可以将大量不确定参数作为输入，重要的是通过全局敏感性分析 (GSA) 确定它们对输出的影响。但是，这些代码可能很耗时，这会阻止基于经典 Sobol' 指数的 GSA，从而需要过多的代码模拟。为了解决这一限制，本文重点关注希尔伯特-施密特独立性准则 (HSIC)，并提出新的面向目标的算法来优化基于 HSIC 的置换独立性测试，以用于筛选和排名目的。基于所研究模拟器的输入/输出样本，基于 HSIC 的测试依赖于独立假设下p值的估计。这些p无论样本大小如何，都可以通过置换方法估计 - 值，但在实践中，基于大量置换的可靠估计可能会令人望而却步。为了克服这个问题，提出了几种策略来贪婪估计p-值，根据 GSA 的最终目标。因此提出了三个顺序置换测试：面向筛选、面向排序和面向排序筛选。这些算法在分析示例上进行了测试和比较，然后应用于模拟核压水反应堆事故场景的热工水力用例。他们的效率和节省时间得到了清楚的证明。此外，通过优化算法进行了计算上易于处理的收敛性研究，以评估结果在用例上的稳健性。