This talk focuses on weighted reduced order methods (w-ROMs) for parametrized advection-dominated Optimal Control Problems (OCP(μμ)s) governed by stochastic Partial Differential Equations. This framework is a powerful tool to reliably fill the gap between the model and an observed solution. Studying such a complicated framework might face two issues: (I) the numerical instabilities due to the advection-dominated context, (II) the computational costs needed for statistical analysis. We tackle them through stabilized offline-online w-ROMs. They exploit the probability distribution of the parameters and the stabilized simulations to build a reduced space where faster (and stabilized) simulations are performed.
[L. Venturi, D. Torlo, F. Ballarin, and G. Rozza, Weighted Reduced Order Methods for Parametrized Partial Differential Equations with Random Inputs. Uncertainty Modeling for Engineering Applications, F. Canavero (ed.), Springer International Publishing, pp. 2740, 2019]
[D. Torlo, F. Ballarin, and G. Rozza, Stabilized Weighted Reduced Basis Methods for Parametrized Advection Dominated Problems with Random Inputs. SIAM/ASA Journal on Uncertainty Quantification, 6(4), pp. 1475-1502, 2018]. The methodology is validated employing several numerical test cases in the steady and time-dependent framework.
[F. Zoccolan, M. Strazzullo and G. Rozza. Stabilized Reduced Order Methods for Advection-Diffusion Optimal Control Problems with random inputs. In preparation, 2022].