Monday, Feb 11, 11:00AM-12:00 Noon, Conference room

February 08, 2019 by Duan Chen
Categories: Spring 2022
Professor Hyungchun Lee of  Dept.  of Mathematics, Ajou University, South Korea
Title: Uncertainty quantification for partial differential equations and their optimal control problems
Abstract: In this talk, we consider UQ (Uncertainty quantification) and  optimal control problems for partial differential equation with random inputs. First we introduce a general approach of studying UQ and then consider some optimal control problems.

To determine an applicable deterministic control $\hat{f}(x)$, we consider the four cases which we compare for efficiency and feasibility. We prove the existence of optimal states, adjoint states and optimality conditions for each cases. We also derive the optimality systems for the four cases. The optimality system is then discretized by a standard finite element method and sparse grid collocation method for physical space and probability space, respectively. The numerical experiments are performed for their efficiency and feasibility.