Stochastic Modeling in High Dimensions

George Em Karniadakis

Abstract: A review of recent advances to stochastic modeling will be presented with application to fluid mechanics, ocean modeling, and biological systems. The main framework is based on Wiener chaos expansions and other extensions that allow us to deal efficiently with multi-dimensional systems at a fraction of computational cost compared to Monte-Carlo simulations. The same stochastic modeling approach allows us to examine the effect of random noise and arbitrary perturbations on the stability of flows and other systems. New approaches to address high dimensionality will be presented including the Wick-Malliavin approximation and the joint response-excitation PDF theory.

Biography: Professor Karniadakis received his B.Sc. from NTU, Athens, Greece in 1982, M.S. from MIT in 1984, and his Ph.D. from MIT in 1987. He was a postdoc at Stanford University (1987-1988) and Assistant Professor at Princeton from 1988-1993; a Visiting Professor at Caltech in the Spring quarter of 1993, an Associate Professor at Brown University from 1994 to 1996 and became a full Professor at Brown University in 1996. He has been a Research Scientist/Senior Lecturer of Mechanical Engineering at the Massachusetts Institute of Technology since 2000. Professor Karniadakis’s main interest is the development of new numerical methods for multiscale modeling of physical and biological systems. He has authored three books and more than 200 research papers. He is a SIAM Fellow, a Fellow of the American Society of Mechanical Engineers, a Fellow of the American Physical Society, and an AIAA Associate Fellow. In 2007 Professor Karniadakis was awarded the 2007 Computational Fluid Dynamics Award presented by the US Association of Computational Mechanics. He is currently a professor of Applied Mathematics at Brown University and a research scientist of Mechanical Engineering at MIT. More information about Dr. Karniadakis can be found at http://www.cfm.brown.edu/people/gk/ and http://seagrant.mit.edu/people_desc.php?ID=265.