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A Dynamically Bi-Orthogonal Method for Time-Dependent Stochastic Partial Differential Equation
Date:2016/5/9     Browse:413

A Dynamically Bi-Orthogonal Method for Time-Dependent Stochastic Partial Differential Equation

Speaker: Zhiwen Zhang

Time: May 9, 10:30am - 11:30am.

Location: Room 405, Administration Center

Abstract:

We propose a dynamically bi-orthogonal method (DyBO) to study time dependent stochastic partial differential equations (SPDEs). The objective of our method is to exploit some intrinsic sparse structure in the stochastic solution by constructing the sparsest representation of the stochastic solution via a bi-orthogonal basis. It is well-known that the Karhunen-Loeve expansion minimizes the total mean squared error and gives the sparsest representation of stochastic solutions. However, the computation of the KL expansion could be quite expensive. In this talk, we derive an equivalent system that governs the evolution of the spatial and stochastic basis in the KL expansion. Unlike other  reduced model methods, our method constructs the reduced basis on-the-fly without the need to form the covariance matrix or to compute its eigen-decomposition. Several numerical experiments will be provided to demonstrate the effectiveness of the DyBO method.

Bio:

Zhiwen Zhang is an assistant professor in the university of Hong Kong. He was a postdoctoral scholar in the Department of Computing and Mathematical Sciences, California Institute of Technology from 2011 to 2015. He graduated from the Department of Mathematical Sciences, Tsinghua University in 2011, where he was awarded the degree of Ph.D. in Applied Mathematics. From 2008 to 2009, he studied in the University of Wisconsin at Madison as a visiting PhD student. His research interests lie in the applied analysis and numerical computation of problems arising from quantum chemistry, wave propagation, porous media, biomechanics, sparse Bayesian learning, and uncertainty quantification (UQ) for stochastic fluid dynamics and random heterogeneous media.

SIST-Seminar 16029