For Zoom Link please contact ddelreyfernandez@uwaterloo.ca

## Speaker

Jan S. Hesthaven, Chair of Computational Mathematics and Simulation Science Ecole Polytechnique Fédérale de Lausanne

## Title

Structure preserving reduced order models

## Abstract

The development of reduced order models for complex applications promises rapid and accurate evaluation of the output of complex models under parameterized variation with applications to problems which require many evaluations, such as in optimization, control, uncertainty quantification and applications where near real-time response is needed. However, many challenges remain to secure the flexibility, robustness, and efficiency needed for general large scale applications, in particular for nonlinear and/or time-dependent problems.

After a brief introduction to reduced order models, we discuss the development of methods which seek to conserve chosen invariants for nonlinear time-dependent problems. We develop structure-preserving reduced basis methods for a broad class of Hamiltonian dynamical systems, including canonical problems and port-Hamiltonian problems, before considering the more complex situation of Hamiltonian problems endowed with a general Poisson manifold structure which encodes the physical properties, symmetries and conservation laws of the dynamics.

Time permitting we also discuss the extension of structure preserving models within a framework for nonlinear reduced order models in which a local basis allows to maintain a small basis even for problems with a slowly decaying Kolmogorov n-width such a transport dominated problems. We shall demonstrate the efficiency of such techniques for nonlinear transport dominated problems, including problems in kinetic plasma physics.

This work is done in collaboration with B, Maboudi (DTU), C. Pagliantini (TU/e), N. Ripamonti (EPFL).