Stabilized Reduced Order Methods for Transport Control Problems with Random Inputs

Gianluigi Rozza (SISSA, Trieste)

May 10. 2022, 11:20 — 12:10

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].

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Computational Uncertainty Quantification: Mathematical Foundations, Methodology & Data (Thematic Programme)
Clemens Heitzinger (TU Vienna)
Fabio Nobile (EPFL, Lausanne)
Robert Scheichl (U Heidelberg)
Christoph Schwab (ETH Zurich)
Sara van de Geer (ETH Zurich)
Karen Willcox (U of Texas, Austin)