Optimal Mass Transport and Density Flows

Speaker: Tryphon Georgiou
Affiliation: University of California Irvine

Abstract:  We will discuss 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. Historically, OMT was introduced by G. Monge in 1781, it was relaxed into a linear programing by L. Kantorovich (1940’s), and then recast as a fluid flow problem by Benamou and Brenier (1990’s). OMT has since been the cornerstone of advances in physics, econometrics, probability theory, and many other fields. Historically, SB’s which amount to a stochastic analogue of OMT, were introduced by E. Schroedinger in 1931 in an attempt to explain Quantum Mechanics in a classical manner and have since proved increasingly pertinent in the same context and for the same applications as OMT. We will explain the connection between the two topics, we will present a numerical scheme for their solution based on a fixed-point iteration (Sinkhorn-like) and the Hilbert metric, and we will highlight the relevance of the two topics in the control of particle ensembles, thermodynamic systems, flows of power spectra, morphing of images. We will also discuss generalizations of OMT and SB’s, first to the setting of a discrete space with applications to the transport of resources over networks and, second, to a non-commutative quantum mechanical setting where we will show that the Lindblad equation of open quantum systems is precisely a quantum-density gradient flow of the von Neumann quantum entropy in a suitable non-commutative Wasserstein geometry.  The talk is based on joint work with Yongxin Chen (MSKCC), Michele Pavon (University of Padova), and Allen Tannenbaum (Stony Brook).

Biography:  Tryphon T. Georgiou is a UCI Chancellor’s Professor in Mechanical and Aerospace Engineering at the University of California, Irvine. He 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).

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).

For more information, contact Prof. Paulo Tabuada ()

Date/Time:
Date(s) - Apr 07, 2017
11:00 am - 12:30 pm

Location:
E-IV Faraday Room #67-124
420 Westwood Plaza - 6th Flr., Los Angeles CA 90095