Collaborative Research: Model Reduction for Probabilistic Analysis and Design Under Uncertainty

Abstract

Abstract : Effective computational tools to support decision-making under uncertainty are becoming essential in the design and operation of aerospace systems. The accurate and efficient propagation of uncertainties in parameters through complex, high fidelity computational models is a significant challenge. Since analytical characterizations of uncertainties in the system outputs are typically not available, numerical methods must be used that require repeated evaluations of models at suitably sampled parameters. Model reduction is a promising technique to substantially reduce the computational cost involved in the propagation of uncertainty. This collaborative project has provided new algorithmic tools and analyses for model reduction of nonlinear systems, demonstrated their application to various systems including uncertainty quantification in chemically reacting flows, and developed adaptive stochastic collocation methods for optimization problems governed by partial differential equations with uncertain inputs.