Stochastic Control and Densities Flows
Feb 6, 2018 | Atlanta, GA
We will talk about two closely related topics, Monge-Kantorovich Optimal Mass Transport (OMT) and Schroedinger's Bridges (SB's). These can be viewed as the stochastic control problems to steer the Liouville and Fokker-Planck equations, respectively, between starting and end-point probability distributions, i.e., the problems to regulate the path of uncertain systems between specified marginals. We will explain the connection between the two topics, present a fast numerical scheme for their solution based on a fixed-point iteration (Sinkhorn-like), and highlight the relevance in applications (thermodynamic systems, spectral analysis, morphing of images, etc). We will also discuss generalizations of OMT and SB's, that include second-order calculus and splines in Wasserstein space (which allows smooth interpolation of densities), transport of vector-valued distributions, transport of resources over networks, and finally quantum mechanics where show that the Lindblad equation is the gradient flow of the von Neumann entropy in a suitably-defined Wasserstein metric.
The talk is based on joint work with Yongxin Chen (MSKCC), Michele Pavon (University of Padova), and Allen Tannenbaum (Stony Brook).
About Dr. Georgiou
Tryphon T. Georgiou received the Diploma in Mechanical and Electrical Engineering from the National Technical University of Athens, Greece, in 1979, and the Ph.D. degree from the University of Florida, Gainesville, in 1983. He served on the faculty of Florida Atlantic University (1983-86), Iowa State University (1986-89) and the University of Minnesota (1989-2016). At Minnesota he held the Hermes-Luh Chair in Electrical Engineering (2002-2016) and was co-director (together with Gary Balas) of the Control Science and Dynamical Systems Center (1990-2016). He is currently a UCI Chancellor’s Professor in Mechanical and Aerospace Engineering at the University of California, Irvine.
Dr. Georgiou has received the George S. Axelby Outstanding Paper award of the IEEE Control Systems Society three times, for the years 1992, 1999, and 2003. He is a Fellow of the Institute of Electrical and Electronic Engineers (IEEE), a Fellow of the International Federation of Automatic Control (IFAC), and a Foreign Member of the Royal Swedish Academy of Engineering Sciences (IVA).