Une nouvelle méthode multi-élément non-intrusive basée sur la clusterisation agglorémative capable d'approcher les systèmes dynamiques bifurcatifs

International audienceA multi-element non-intrusive generalised polynomial chaos method is developed to approximate state variable of a bifurcative dynamical system. It rely on a partitioning of the stochastic space along discon-tinuities of any shapes, efficient even when the discontinuities are running partially, and allowing the use of a low degree of approximation. An agglomerative clustering method is implemented in a space defined by the values of the quantity of interest (QOI) and of its derivatives with respect to the stochastic parameters. The stochastic space is first properly sampled. Then, at every instant, several partitions of the stochastic space are tested and the best one is selected as the one minimizing the maximum of the cross-validation errors of the local surrogate models. Once the local models are obtained and the sto-chastic space is correctly sliced, a neural network classifier is learned to determine in which element a sample is for further evaluations at the considered instant. The method uses the same samples for the space partitioning and for the training of the local models with regression thus reducing the computational cost. The long-time integration problem is countered and the stochastic space can be split according to the discontinuity induced by the potential bifurcation. The results of the method are advantageously compared to those obtained with the direct use of a Gradient Tree Boosting algorithm at every instant and the classical Pseudo projection method for a system leading to a bifurcation