In this paper, we propose a new methodology for solving stochastic inversion problems through computer experiments, the stochasticity being driven by a functional random variables. This study is motivated by an automotive application. In this context, the simulator code takes a double set of simulation inputs: deterministic control variables and functional uncertain variables. This framework is characterized by two features. The first one is the high computational cost of simulations. The second is that the probability distribution of the functional input is only known through a finite set of realizations. In our context, the inversion problem is formulated by considering the expectation over the functional random variable. We aim at solving this problem by evaluating the model on a design, whose adaptive construction combines the so-called Stepwise Uncertainty Reduction (SUR) methodology with a strategy for an efficient expectation estimation. Two greedy stategies are introduced to sequentially estimate the expectation over the functional uncertain variable by adaptively selecting curves from the

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. This is all the more true as the number of inputs is important. To address this limitation, we consider recent advances in dependence measures, focusing on the Hilbert-Schmidt independence criterion (HSIC). In this framework, this paper proposes new goal-oriented algorithms to optimize the permuted HSIC-based tests for screening and ranking purposes.HSIC-based tests are built upon a sample of inputs/output of the studied model (simulator) and relies on the estimation of a p-value under independence hypothesis. These p-values can be estimated either by an asymptotic approximation (for large sample size) or by permutation method. However in the latter case, a brute approach with a large number of permutations can be prohibitive in practice, especially when the testing procedure is repeated a large number of times. To overcome this, we propose several strategies 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-screeningoriented. These algorithms are tested and compared on analytical examples. The performances in terms of accuracy, efficiency and time saving are clearly demonstrated. Their use is then illustrated on a nuclear engineering use case simulating an intermediate-break loss-of-coolant accident on a pressurized water reactor. A convergence study, made computationally tractable by the optimized algorithms, is carried out to assess the convergence of the results, according to the sample size.