The Mini-course “Uncertainty Quantification and Approximation Theory for Parameterized PDEs”, lectured by Prof. Clayton G. Webster, Dr. Hoang Tran, and Dr. Guannan Zhang (Oak Ridge National Laboratory, USA), started at VIASM on November 14, 2016. This Mini-course will last until November 17, 2016.
In this course, the lectures present a general class of numerical methods and analysis for simultaneously approximating a system of partial differential equations (PDEs), parameterized by many deterministic (e.g., spatial position, and velocity) and stochastic variables, ranging over a multi-dimensional domain, where the parametric dimension can be very large, or even infinite.
This tutorial explores numerical and functional analysis techniques for solving such problems, including well-posedness and regularity of the resulting parameterized PDE problems. They also present a detailed overview and convergence analysis of several methods for quantifying the uncertainties associated with input information onto desired quantities of interest, forward and inverse uncertainty quantification (UQ) approaches, and necessary theoretical results from stochastic processes and random fields, error analysis, anisotropy, adaptive methods, high-dimensional best s-term approximation, compressed sensing, discrete least squares, deterministic and random sampling, and sparse grids.
There are nearly 30 participants in the first day of the course.