Optimized HSIC‐based Tests for Sensitivity Analysis: Application to Thermalhydraulic Simulation of Accidental Scenario on Nuclear Reactor

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.