Data-based reductions and closure models for dynamical systems

Abstract: The reduced-order description of physical systems from observed data is an important component in the analysis of many dynamical processes occurring in nature. In the first part of this talk, we will introduce a data-based reduction using transfer operators and graph theory, which will result in a Markov-model description of the underlying process. It will be exemplified on a magnetic Taylor-Green model for the Earth's magnetic field reversal. The second part will address the stability of closure approaches in highly truncated model reductions. A residualization, rather than truncation, technique will be discussed and applied to the closure of the harmonically balanced Navier-Stokes equations using a machine-learning approach.

Bio: Peter Schmid currently holds a Professorship of Mechnical Engineering at the King Abdullah University of Science and Technology (KAUST). Before joining the department in 2021, he held positions as Chair Professor of Applied Mathematics at Imperial College London, and before then, as research director with the French National Research Agency (CNRS) together with a professorship (PCC) at the Ecole Polytechnique in France. He started his career as a faculty member in Applied Mathematics at the University of Washington in Seattle, WA. He received his Ph.D. in Mathematics from M.I.T. and his Engineer’s Degree in Aerospace Engineering from the Technical University Munich. His research lies in the area of computational fluid dynamics, with emphasis on stability theory, receptivity analysis, flow control, model reduction and system identification. He is also interested in methods for quantitative flow analysis for numerical and experimental data.