IRTG Modern Inverse Problems (MIP)
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SSD Seminar Series with Prof. Ramon Codina, Ph.D.

9. November 2020 @ 16:00 - 17:00

Dr. Ramon Codina, Ph.D. – Reduced Order Models for Flow Problems: Stabilization and Accuracy Enhancement


University of Politècnica de Catalunya, Spain




Reduced Order Models (ROM) in computational mechanics aim at solving problems approximating the solution in spaces of very low dimension. The idea is to solve first the Full Order Model (FOM) in a high-fidelity space, of high dimension, extracting the main features of the solution and, from these, construct the basis of the ROM space. In this talk we shall concentrate on the case in which the FOM is solved by means of a Finite Element (FE) method and the ROM is obtained from a Proper Orthogonal Decomposition (POD) of a series of ’snapshots‘, i.e., high-fidelity solutions obtained for example at different time instants or for different values of a parameter of the problem to be solved. This way, the ROM solution can be considered to belong to a subspace of the FOM FE space, but defined on the same FE mesh.

The Variational Multi-scale (VMS) concept applied to the approximation of boundary value problem is quite simple. The idea is to split the unknown into the resolvable component, in our case living in the FE space, and a remainder, called sub-grid scale (SGS). After setting a problem for the SGS, this problem is what is in fact approximated somehow, so that the SGS can be expressed in terms of the FE solution. When the resulting expression is inserted into the equation projected into the FE space, one ends up with a problem for the FE unknown with enhanced stability problems. This idea is mainly used for the space approximation, being finite differences the most common option in time. The first purpose of this talk is to explain why the VMS strategy can be applied quite naturally to the ROM approximation when this is based in a FE method to approximate flow problems. This yields a stable ROM problem.


The second objective of the talk is to explain how accuracy can be improved using Artificial Neural Networks (ANN). Motivated by the structure of the stabilization terms arising from VMS, an additional correcting term is added to enhance accuracy. This term is an ANN trained with the snapshots, i.e., the high-fidelity solutions used to construct the basis of the ROM.


9. November 2020
16:00 - 17:00


a link for the Zoom meeting room will be send in the newsletter one week before the seminar starts. If you want to participate, please send an email to office@aices.rwth-aachen.de to get the zoom link.