Uncertainty Quantification in Scientific Computing

Computing has become an indispensable component of modern science and engineering research. This may be viewed as a natural legacy of Moore’s Law. As has been repeatedly observed and documented, processing speed measured in floating point operations per second has experienced exponential growth for several decades. To a large degree, hardware efficiencies have been accompanied by innovations in programming languages, mathematical algorithms, and numerical software. The result is that, by any measure, the modern computer is many orders of magnitude more powerful than its early predecessors, capable of simulating physical problems of unprecedented complexity. In short, it would appear that the “Performance Challenge”—designing and building high performance computers for scientific computation—is largely being met [4]. Given computing’s success as a research tool, it is natural that scientists, engineers, and policy makers attempt to harness this immense potential by using computational models for critical decision-making, e.g., to supplement experiments, to prototype engineering systems, or to predict the safety and reliability of highconsequence systems. However, there is a barrier in this use which takes the form of a simple question, “How good are these simulations?” The simplicity of the question is deceptive. It can be interpreted as one of accuracy assessment and its counterpart quantification of uncertainty (UQ). How should