MEAM Seminar: “Structure Preserving Reduced Order Models”
April 6 at 10:30 AM - 12:00 PM
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.
This work is done in collaboration with B. Maboudi (Stuttgart), C. Pagliantini (TU/e), N. Ripamonti (EPFL).
Jan S. Hesthaven
Professor of Mathematics and Chair of Computational Mathematics and Simulation Science, EPFL, Lausanne, Switzerland
After receiving his PhD in 1995 from the Technical University of Denmark, Professor Hesthaven joined Brown University, USA where he became Professor of Applied Mathematics in 2005. In 2013 he joined EPFL as Chair of Computational Mathematics and Simulation Science and from 2017-2020 as Dean of the School of Basic Sciences. From 2021, he serves as Provost at EPFL and on the Board of Trustees of SIAM.
His research interests focus on the development, analysis, and application of high-order accurate methods for the solution of complex time-dependent problems, often requiring high-performance computing. A particular focus of his research has been on the development of computational methods for problems of linear and non-linear wave problems and the development of reduced basis methods, recently with an emphasis on combining traditional methods with machine learning and neural networks with broad applications, including structural health monitoring.
He has received several awards for both his research and his teaching, and has published 4 monographs and more than 160 research papers. He is on the editorial board of 8 journals and since 2016 has served as Editor-in-Chief of SIAM J. Scientific Computing.
Homepage – https://www.epfl.ch/labs/mcss/