Séminaire de l’équipe MCS
Responsables : M. DARBAS, E. AUDUSSE
Lundi 12 mai 2025
11:00 Anca Belme (Sorbonne Université, Institut d'Alembert) 
Résumé
Solving stochastic inverse problems for CFD using data-consistent inversion and an adaptive stochastic collocation method
Salle B405, bâtiment B, LAGA, Institut Galilée, Université Paris 13The recent development of data-driven approaches has increased interest in developing robust and efficient algorithms to exploit data in engineering design and modelling in CFD. A common set of oberved data d can be some function of a system output, or some desired (targeted) data. A frequent question then arises: what should be the model input that gives as output the targeted or observed data. Solving such inverse problems using a high-fidelity CFD model is very expensive in computational time and storage. This cost is even more important if the CFD model is subject to uncertainties. We are often interested in a model output, defined as a quantity of interest (QoI) whose value, while in presence of uncertainties, will no longer be a scalar but a functional depended on the uncertain parameters. Besides the cost of high-fidelity CFD problems in presence of numerical uncertainties, the model must accurately describe highly nonlinear flow dynamics (like shock waves, etc). The inverse problem we consider here takes a given model and an observed (targeted) output probability density function (pdf) on QoI, and builds a new model input pdf which is consistent with both the model and the data in the sense that the push-forward of this pdf through the model matches the given observed pdf. We present in this work a non-intrusive adaptive stochastic collocation method coupled with a data-consistent inference framework of to efficiently solve stochastic inverse problems in CFD. This adaptive surrogate model is built using a stochastic error estimator as refinement indicator in simplex elements. The efficiency of the proposed method is evaluated on analytical test cases and two CFD configurations. The proposed method is shown to be able to reconstruct both an observed pdf on the data and key components of a data-generating distribution in the uncertain parameter space.
Lundi 26 mai 2025
11:00 Chien-Hong Cho (National Sun Hat-sen University, Taiwan ) Résumé
A numerical algorithm for blow-up problems
Salle B405, bâtiment B, LAGA, Institut Galilée, Université Paris 13Solutions of initial value problems do not always exist globally in time and may become unbounded in a finite time. Such a phenomenon is often referred to as blow-up and the finite time is often called the blow-up time. To construct a numerical solution which also blows up in a finite time, adaptive temporal strategies were considered to be necessary. The approximate blow-up times, however, are usually defined by infinite sums, which cannot be carried out in real computation. As a result, we reconsider the schemes with uniform time meshes and propose an algorithm to compute an approximate blow-up time, which can be achieved concretely with rigorous convergence proofs. We will introduce the idea via a simple ODE blow-up problem and several applications for the computation of certain blow-up behaviors to PDE problems will be explored, too. Furthermore, such an idea is also applicable to the algorithms with adaptive temporal grids. Remarks on this issue will also be addressed.
Lundi 16 juin 2025
11:00 Félix Kwok (Université de Laval )
Titre bientôt disponible
Salle B405, bâtiment B, LAGA, Institut Galilée, Université Paris 13
