The AFOSR MURI project on Uncertainty Quantification seeks to develop rigorous theory, algorithms and software for UQ management in a computationally scalable way.  Our effort is to demonstrate how a mathematical framework that addresses the analysis of stochastic multiscale systems can be driven by limited/gappy information, and lead to a revolutionary but realistic approach for capturing, harnessing and exploiting stochasticity in engineered systems.  Our goal is to demonstrate the physical relevance and broad applicability of our framework through the consideration of multiple applications of interest to the USAF.

The present project, "Multi-Scale Fusion of Information for Uncertainty Quantification and Management in Large Scale Simulation" implements a robust integrated methodology, and is comprised of five major research areas:  (1) Mathematical analysis and multiscale formation of SPDEs, (2) Numerical solution of SPDEs, (3) Dimension reduction, (4) Multiscale property estimation, and (5) Design and control under uncertainty.