$School of Mathematical and Statistical Sciences$

Computational and Applied Math Proseminar

Tuesday, November 10, 12:00 p.m. ECG 317

Dongbin Xiu

Purdue University

Uncertainty Analysis for Complex Systems: Algorithms and Data

Abstract The field of uncertainty quantification has received increasing amount of attention recently. Extensive research efforts have been devoted to it and many novel numerical techniques have been developed. These techniques aim to conduct stochastic simulations for large-scale complex systems.

In this talk we will review one of the most widely approaches -- generalized polynomial chaos (gPC). The gPC based methods employ orthogonal polynomials in random space and take advantage of the solution smoothness (whenever possible). The features of various gPC numerical schemes will be reviewed. Furthermore, we will discuss how real observational data can be utilized and combined with stochastic simulations. The resulting data-driven uncertainty analysis can provide much more insight to the true physics and produce predictions of high fidelity.