Colloquium

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 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 some of the highly efficient algorithms that are based on gPC and effective for simulations beyond uncertainty propagation. These algorithms are applicable for problems such as inverse inference, data assimilation, reliability analysis, etc.