Collaborative Research Model Reduction for Nonlinear and Parametric Systems with Uncertainty

Abstract : This project has developed and analyzed new mathematical algorithms to substantially reduce the complexity of simulating and optimizing parametrically dependent systems and to support decision-making under uncertainty. Specifically, this research has advanced the state of the art in reduced order modeling based on projections and on the discrete empirical interpolation method (DEIM) for nonlinear systems, developed new adaptive sampling methods for optimization of systems with uncertain inputs, devised a domain decomposition based methods to systematically integrate the uncertainty propagation through components into uncertainty propagation through a systems composed of these components, established a so-called CUR factorization based on the DEIM that provides a low rank approximate factorization of a given large matrix with applications to POD model reduction and analysis of data. The feasibility of our algorithms was demonstrated on a number of problems with relevance to the Air Force.