No Equations, No Variables: A Computer-assisted Approach to Modeling Complex/Multiscale Systems

Friday, March 20, 2015
230E Gross Hall -  11:00 A.M.

Yannis Kevrekidis, PhD

Professor CHemical and Biological Engineering, Princeton University 


In current modeling practice for complex systems/multiscale systems the best available descriptions of a system often come at a fine level (atomistic, stochastic, microscopic, individual-based) while the questions asked and the tasks required by the modeler (prediction, parametric analysis, optimization and control) are at a much coarser, averaged, macroscopic level.

Traditional modeling approaches start by first deriving macroscopic evolution equations from the microscopic models, and then bringing our arsenal of mathematical and algorithmic tools to bear on these macroscopic descriptions.

Over the last few years, and with several collaborators, we have developed and validated a mathematically inspired, computational enabling technology that allows the modeler to perform macroscopic tasks acting on the microscopic models directly. We call this the ``equation-free” approach, since it circumvents the step of obtaining accurate macroscopic descriptions.

Ultimately, what makes it all possible is the ability to initialize computational experiments at will. Short bursts of appropriately initialized computational experimentation ­through matrix-free numerical analysis and systems theory tools like variance reduction and estimation- bridges microscopic simulation with macroscopic modeling.

I will discuss the approach and illustrated through several applications in science and engineering; I will also discuss how to link the approach with recent developments in data mining algorithms, exploring large complex data sets to find good "reduction coordinates".

In a sense, the approach could be thought of as a data-based calculus for the modeling of complex systems

Biolographical Sketch

Yannis Kevrekidis studied Chemical Engineering at the National Technical University in Athens. He then followed the steps of many alumni of that department to the University of Minnesota, where he studied under the supervision of Rutherford Aris and Lanny Schmidt.

He also worked with Dick McGehee and Don Aronson in the Mathematics Department on computational studies of dynamical systems, something that still remains the main theme of his research. He was a Director's Fellow at the Center for Nonlinear Studies in Los Alamos in 1985-86.

He has been at Princeton since 1986, where he teaches Chemical Engineering and also Applied and Computational Mathematics. His research interests are centered around the dynamics of physical and chemical processes, types of instabilities, pattern formation, and the ways to study and understand such phenomena computationally. In recent years he has also developed an interest in multiscale computations. He has been a Packard Fellow, a Presidential Young Investigator, and the Ulam Scholar at Los Alamos National Laboratory. He holds the Colburn and Wilhelm Awards of the AIChE, the Crawford prize of SIAM and a Humboldt Prize.