Maseeh Mathematics and Statistics Colloquium Series

Speaker: Dr. Joel A. Rosenfeld

Title: The Kernel Perspective on Dynamic Mode Decompositions

Abstract: The system identification (or approximation) problem is the determination of an accurate approximation of a dynamical system from observations of the state or output. In this talk we discuss the role operators and reproducing kernel Hilbert spaces play in nonlinear system identification and modeling problems. This is directly connected to the Koopman operator framework that has recently become popular. I will present the advantages that come with the kernel perspective, as well as a pointwise convergent result that comes from the use of compact operators.

Biography: Dr. Joel A. Rosenfeld is an Assistant Professor in the Department of Mathematics and Statistics at the University of South Florida and the Principal Investigator of the Learning DOCK Group. He received his Ph.D. from the mathematics department at the University of Florida in 2013 under the advisement of Dr. Michael T. Jury studying Operator Theory and Functional Analysis. Following graduate school, he was a postdoc in Mechanical Engineering at the University of Florida under Dr. Warren E. Dixon studying numerical methods in optimal control theory and fractional calculus. Subsequently, he joined the Department of Electrical Engineering and Computer Science at Vanderbilt University under Dr. Taylor T. Johnson studying numerical methods in formal methods for computing, which ultimately led to a position as a Senior Research Scientist Engineer within the Institute for Software Integrated Systems (ISIS). Dr. Rosenfeld is a Young Investigator Research Program (YIP) awardee through the Air Force Office of Scientific Research (AFOSR) (awarded in 2020).