Koopman Operator Theory Based Machine Learning of Dynamical Systems

Professor Igor Mezić,
University of California, Santa Barbara

Many approaches to machine learning have struggled with applications that possess complex process dynamics. In contrast, human intelligence is adapted, and - - arguably - built to deal with complex dynamics. The current theory holds that human brain achieves that by constantly rebuilding a model of the world based on the feedback it receives. I will describe an approach to machine learning of dynamical systems based on Koopman Operator Theory (KOT) that also produces generative, predictive, context-aware models amenable to (feedback) control applications. KOT has deep mathematical roots and I will discuss its basic tenets. I will also present computational methods that enable lean computation. A number of examples will be discussed, including use in fluid dynamics, power grid dynamics, network security, soft robotics, and game dynamics.

Acknowledgement:
Support from ARO, AFOSR, DARPA, NSF and ONR is gratefully acknowledged.

Professor Igor Mezić's Biography:
Ph.D., 1994, Applied Mechanics
California Institute of Technology
Dipl. Ing., 1990, Mechanical Engineering
University of Rijeka, Croatia

Professor Mezic works in the field of artificial intelligence (AI), dynamical systems, control theory and applications to security, energy efficient design, soft robotics, quantum mechanics and operations in complex systems. He did his Ph. D. in Dynamical Systems at the California Institute of Technology. Dr. Mezic was a postdoctoral researcher at the Mathematics Institute, University of Warwick, UK in 1994-95. From 1995 to 1999 he was a member of College of Engineering at the University of California, Santa Barbara where he is currently a Distinguished Professor. In 2000-2001 he has worked as an Associate Professor at Harvard University in the Division of Engineering and Applied Sciences. He won the Alfred P. Sloan Fellowship, NSF CAREER Award from NSF and the George S. Axelby Outstanding Paper Award from IEEE. He also won the United Technologies Senior Vice President for Science and Technology Special Achievement Prize in 2007. For his work on analysis and control of complex systems, he was named Fellow of the American Physical Society, Fellow of the Society for Industrial and Applied Mathematics and Fellow of the Institute of Electrical and Electronics Engineers. He is the recipient of the 2021 Crawford Prize, awarded once in two years to a researcher in Dynamical Systems Theory. Dr. Mezic is the Director of the Center for Energy Efficient Design and Head of Buildings and Design Solutions Group at the Institute for Energy Efficiency ay the University of California, Santa Barbara. He holds 10 US patents. He founded Aimdyn, Inc. in 2003 and is the co-founder, CTO and Chief Scientist of Mixmode.ai.