Challenge problems: uncertainty in system response given uncertain parameters

Modeling and simulation efforts continue to expand in areas where they have been used for some time, and they are also beginning to be used in new application areas. Modeling and simulation have been heavily used in risk assessment for high-consequence systems, such as nuclear power reactors, underground storage of radioactive wastes, and the nuclear weapon stockpile. For complex engineered or natural systems, computer-based modeling and simulation is required. Most of the mathematical models of these physical systems are given by systems of coupled partial differential equations (PDE). For example, typical computer codes which numerically solve these PDEs, and all of their auxiliary equations, can contain tens to hundreds of thousands of lines of code. Similarly, the inputs and outputs of these codes have high dimensionality, for example, hundreds of input and output quantities.