## Applied Mathematics Colloquium: Dr. Heyrim Cho

#### University of Maryland, College Park

**Title:** Numerical methods for
uncertainty quantification - from noise parameterization to efficient
simulation of parameterized stochastic PDE

**Speaker: **Heyrim Cho, University of Maryland, College Park

**Abstract: **For a reliable
simulation of systems subject to noise, it is necessary to characterize the
noise properly and develop efficient algorithms. In the first part of this
talk, I will present a numerical technique to model and simulate multiple
correlated random processes. The method finds the appropriate expansion for
each correlated random process by generalizing the Karhunen-Loeve (K-L)
expansion, in particular, by releasing the bi-orthogonal condition of the K-L
expansion. I will address the convergence and computational efficiency, in
addition to some explicit formulae and analytical results. In the second part,
I will present an adaptive reduced basis method that enables an efficient
simulation of parameterized stochastic PDEs. The method is employed by using an
adaptive ANOVA and probabilistic collocation method to automatically identify
the important dimensions and appropriate resolution in each dimension. The
effectiveness of the method is demonstrated in anisotropic high-dimensional
stochastic PDEs.