Dr Heyrim Cho
Division of Applied Mathematics - Brown University
High-dimensional Numerical schemes and Dimension Reduction techniques for Uncertainty Quantification based on Probability Density Functions
Thursday, May 14, 2015, 4:00pm to 5:00pm | Room 3-133
Probability density functions (PDFs) provide the entire statistical structure of the solution to stochastic systems. In this talk, we introduce the joint response-excitation PDF approach that enables us to do stochastic simulations based on PDFs with various type of randomness involving non-Gaussian non-Markovian colored noise. We develop efficient numerical algorithms to solve this system in high-dimensions. In particular, we develop high-dimensional numerical schemes by using ANOVA approximation and separated series expansion. Alternatively, we employ dimension reduction techniques such as conditional moment closures and Mori-Zwanzig approach to obtain reduced order equations. These methodologies can be applied in general to stochastic systems to overcome high-dimensionality. The effectiveness of our approach is demonstrated in various stochastic dynamical systems and stochastic PDEs, including Lorenz 96 system and Burgers equation yielding multiple interacting shock waves at random space-time locations.
Heyrim Cho received her B.S. degree in Applied Mathematics at KAIST, Korea in 2007 and her M.S. degree in Mathematics at the same institution in 2009. Her masters research was on numerical schemes for PDE and parallel implementation. She has recently defended her Ph.D thesis in the Division of Applied Mathematics at Brown University advised by Professor George Karniadakis, and will be at the University of Maryland as a Brin postdoc fellow starting from the next semester. Her research interest is in stochastic modeling and simulations particularly in high-dimensional and multi-scale systems.