MCS - Seminar

Tuesday 04 December 2024 

SPEAKER:  Yvo Boers
Location: RAV 2503

TITLE:  Various Notes on Convergence Results forParticle Filtering: Theory and Practice

ABSTRACT: 

We discuss  fundamental results in the field of particle filtering and their implications for practitioners and theoreticians alike . These results were already being used by practitioners in different applications; before they actually had been proven formally in the appropriate theoretical framework.

Some fundamental results, discussed here, are versions of Laws of Large Numbers for Particle Filters(PFs), related to different convergence results for PFs. 

Some new results are also presented here. As well as results, that allow the use of empirical expectations for a certain class of unbounded functions and its corresponding convergence to the true expectation, are discussed.

Examples will be provided throughout the presentation.

Tuesday 05 November 2024 16:00 - 17:15 hrs

SPEAKER:  Jan-Frederik Pietschmann https://www.uni-augsburg.de/de/fakultaet/mntf/math/prof/invpde/team/jan-f-pietschmann/

Location: RAV 2504

TITLE:  DATA-DRIVEN GRADIENT FLOWS

ABSTRACT:
We present a framework enabling variational data assimilation for gradient flows in general spaces, metric based on the minimizing movement (or Jordan–Kinderlehrer–Otto) approximation scheme. After discussing stability properties in the most general case, we specialize to the space of probability measures endowed with the Wasserstein distance.  This setting covers many non-linear partial differential equations (PDEs), such as the porous-medium equation or general drift–diffusion–aggregation equations, which can be treated by our methods independently of their respective properties (such as finite speed of propagation or blow-up).
We then focus on the numerical implementation using a primal–dual algorithm. This setting covers many non-linear partial differential equations (PDEs), such as the porous-medium equation or general drift–diffusion–aggregation equations, which can be treated by our methods independently
of their respective properties (such as finite speed of propagation or blow-up). We then focus on the numerical implementation using a primal–dual algorithm.

The strength of our approach lies in the fact that, by simply changing the driving functional, a wide range of PDEs can be treated without the need to adopt the numerical scheme.

We conclude by presenting several numerical examples

Tuesday 03 September 2024 16:00 - 17:15 hrs

SPEAKER:  Fernando José Henriquez Barraza
Location: RAV 2231

TITLE:  Model of Reduction for Time-Dependent Problems Using the Laplace Transform Joint work with Jan S. Hesthaven (EPFL)    

ABSTRACT:

We present a novel, fast solver for the numerical approximation of linear, time-dependent partial differential equations based on model order reduction techniques and the Laplace transform. 

We start by applying said transform to the evolution problem, thus yielding a time-independent boundary value problem solely depending on the complex Laplace parameter and the problem's data.

In an offline stage, we carefully sample the Laplace parameter and solve the underlying collection of high-fidelity problems. Next, we apply a proper orthogonal decomposition (POD) to this collection of solutions in order to obtain a basis of reduced order. We project the linear evolution problem onto this basis, and then we solve it using any suitable time-stepping method. We further discussed the applicability of this method to parametric problems. Numerical experiments for parabolic problems and the second-order wave equation portray the performance of the method in terms of accuracy and, in particular, speed-up when compared to standard methods.

• 24 October 2024

Speaker: Wouter Edeling  https://www.cwi.nl/en/people/wouter-edeling/

Title: Forward uncertainty quantification in high dimensions

Abstract:

Dr Wouter Edeling is a tenured researcher in the Scientific Computing group at CWI. He has a background in aerospace engineering, and obtained a joint-PhD from Delft University of Technology and Arts et Métiers ParisTech in 2015 

on the topic of uncertainty quantification for Reynolds Averaged Navier-Stokes (RANS) turbulence closures. He is a recipient of the Center for Turbulence Research Postdoctoral fellowship at Stanford University. 

He has worked on physical model error representation in turbulence models, use of advanced Bayesian data analysis such as Bayesian model scenario averaging, and reduced order modelling of unresolved scales. 

His current research interest lies at the intersection of machine learning, physical models and uncertainty quantification.

• 19 September 2024

Speaker: Karen Veroy - https://www.tue.nl/en/research/researchers/karen-veroy-grepl

Title: Advances, opportunities, and challenges for parametric model order reduction in digital twins

Abstract:

In this talk, we will summarize some recent developments as well as opportunities and challenges in the use of projection-based model order reduction (MOR) for parametrized PDEs in the context of digital twins.  In the first part, we consider the development of (a) reduced-order models (ROMs) for multi-scale problems in solid mechanics and (b) sampling strategies for the construction of ROMs in problems with high-dimensional parameters.  In the second part, we consider challenges in the use of ROMs digital twins, for example in data assimilation, Bayesian inverse problems, and optimal sensor placement.