Minicourse Schedule
2019年4月23日（周二）     15:00-17:00
2019年4月25日（周四）     15:00-17:00

Abstract: Parametric partial differential equations (PDEs) arise from various fields of computational engineering and sciences, in which the parameters may represent initial/boundary conditions, material properties, external loadings, computational geometries, etc. Parametric PDEs serve as the core building block (state/forward/inner problem) for problems of uncertainty quantification, risk/sensitivity analysis, Bayesian inversion, optimal control/design, optimal experimental design, data assimilation, etc., which all involve many-times solution of the parametric PDEs. When the parameters are high or even infinite dimensional, it is a critical challenge to solve the parametric PDEs because of the curse-of-dimensionality, i.e., the computational complexity grows too rapidly, e.g., exponentially, with respect to the dimension of the parameters for many conventional methods, which become intractable for such problems.  In this short course, I will present three approximation methods that can effectively break this curse by exploiting the smoothness, sparsity, and intrinsic low-dimensionality of the parametric PDEs. The lectures are structured as follows:
Lecture 1: Parametric PDEs
Lecture 2: Sparse polynomial approximation