IAM – PIMS Distinguished Colloquium: Tao Tang

Uncertainty quantification (UQ) has been a hot research topic recently. UQ has a variety of applications, including hydrology, fluid mechanics, data assimilation, and weather forecasting. Among a large number of approaches, the high order numerical methods have become one of the important tools; and the relevant computational techniques and their mathematical theory have attracted great attention in recent years. This talk begins with a brief introduction to recent developments of high order numerical methods including Galerkin projection methods and stochastic collocation methods. The emphasis will be sample-based stochastic collocation methods, including random sampling, deterministic sampling and structured random sampling. We will also discuss approximating multivariate functions in unbounded domains by using discrete least squares projection with random point evaluations. Particular attention is given to functions with random Gaussian or gamma parameters.