TITLE
Learning the Koopman Operator for Dynamic Data 

ABSTRACT

Recent work in the study of dynamic systems has focussed on data-driven decomposition techniques that approximate the 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. 

In this talk, I shall briefly summarize the large existing work on data-driven learning of Koopman operator models, and then describe new sampling-based sketching approaches (SketchyCoreSVD, SketchyCoreTucker)  together with matrix-valued Kernels, to achieve accelerated Koopman operator approximations of dynamic observable data. Examples are drawn from remote sensing and FTIR  hyperspectral tensor images, bio-medical cardiac magnetic resonance video, and time series reactive flow simulations of a single ejector combustion process. 
 

BIO
Chandrajit Bajaj is the Computational Applied Mathematics Chair in Visualization, professor of computer science, and director of the Center for Computational Visualization at the University of Texas at Austin. Bajaj earned his undergraduate degree in electrical engineering from the Indian Institute of Technology, and his master's and Ph.D. in computer science from Cornell University. He is an IEEE, ACM, and AAAS Fellow, and has won numerous best paper awards throughout his career. Bajaj has also served as the editor of various publications including ACM Computing Survey, SIAM Journal on Imaging Sciences, and the International Journal of Computational Geometry and Applications. He has authored several books.