Recent work in the study of dynamic systems has focussed on data driven decomposition techniques that approximatethe action of the Koopman operator on observable functions of the underlying phenomena. 

In particular, the data driven method of dynamic mode decomposition (DMD) has been explored, with multiple variants of the algorithm in existence, including extended DMD, DMD in reproducing kernel Hilbert spaces, a Bayesian framework, a variant for stochastic dynamical systems, and a variant that uses deep neural networks. 

The goal in this talk, is to briefly summarize the existing work on data driven learning of Koopman operator models, and then describe a new matrix sketching approach (SketchyCoreSVD)  that guarantees operator  accuracy vs speed tradeoffs. Examples are drawn from bio-medical cardiac magnetic resonance  imaging  (video), and time series simulations of a single ejector  combustion process. I shall highlight accelerated variants of the machine learning algorithms as well as directions for potential future work.

Chandrajit  Bajaj  is the director of the Center for Computational Visualization, in the Institute for Computational and Engineering Sciences (ICES) and a Professor of Computer Sciences at the University of Texas at Austin.  Bajaj holds the Computational Applied Mathematics Chair in Visualization. He is also an affiliate faculty member of  Mathematics, Computational Neuroscience and Electrical Engineering. He is currently on the editorial boards for the International Journal of Computational Geometry and Applications, and the ACM Computing Surveys, and past editorial member of the SIAM Journal on Imaging Sciences.  He was awarded a distinguished alumnus award from the Indian Institute of Technology, Delhi, (IIT, Delhi). He is also a Fellow of The American Association for the Advancement of Science (AAAS), Fellow of the Association for Computing Machinery (ACM), Fellow of the Institute of Electrical and Electronic Engineers (IEEE), and Fellow of the Society of Industrial and Applied Mathematics (SIAM).