Title: Uncertainty Quantification and Bayesian Inversion for High-dimensional Complex Systems with Multimodal Distribution
Speaker: Guang Lin (Purdue University)
Abstract: Experience suggests that uncertainties often play an important role in quantifying the performance of complex systems. Therefore, uncertainty needs to be treated as a core element in modeling, simulation and optimization of complex systems. The field of uncertainty quantification (UQ) has received an 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 very large-scale complex systems.
In this talk, we will present some effective new ways of dealing with the “multi-modal” challenge. Particularly, adaptive importance sampling techniques will be discussed in some detail. Following Bayes' rule, a general approach for inverse modeling problems is to sample from the posterior distribution of the uncertain model parameters given the observations. However, the large number of repetitive forward simulations required in the sampling process could pose a prohibitive computational burden. This difficulty is particularly challenging when the posterior is multimodal. We present an adaptive importance sampling algorithm to tackle these challenges. Several specific examples on flow and transport in randomly heterogeneous porous media will be presented to illustrate the main idea of our approaches.
Seminar URL: https://people.math.osu.edu/xue.41/AppliedMathSeminar.html