Learning reduced dynamical-system models from data via operator inference and Loewner interpolation
Benjamin Peherstorfer, Assistant Professor, Courant Institute of Mathematical Sciences, New York University
3:30 – 5PM
Tuesday Mar 5, 2019
Learning models from data typically means fitting coefficients (weights) of linear combinations of basis (activation) functions to data. In many situations, no particular meaning can be associated with the fitted coefficients of the linear combinations, which means that the learned models predict quantities of interest in black-box ways; however, in science and engineering applications, interpreting models in terms stability, passivity, controllability, attractors, eigenmodes, and other concepts from systems & control theory is critical for guaranteeing the integrity of the overall scientific process. In this presentation, we approach the problem of learning dynamical-system models from the perspective of data-driven model reduction. Instead of fitting linear combinations of basis functions to data, we aim to learn (reduced) operators that describe the dynamics of the systems of interest and so establish notions of systems & control theory concepts for the learned models. We survey recent advances in data-driven model reduction and discuss operator inference and the Loewner framework in detail. Numerical results demonstrate the success of these data-driven model reduction methods and show current limitations and open questions.
Benjamin Peherstorfer is Assistant Professor at Courant Institute of Mathematical Sciences, New York University since 2018. He was Postdoctoral Associate in the Aerospace Computational Design Laboratory (ACDL) at the Massachusetts Institute of Technology (MIT), working with Professor Karen Willcox, and received his Ph.D. degree in computer science from the Technical University of Munich (Germany). Benjamin's current research focus is on computational methods for data- and compute-intensive scientific computing applications, including computational statistics, mathematics of data science, model reduction, uncertainty quantification, and Bayesian inference.