|Date||Apr 26, 2018|
We consider the determination of statistical information about outputs of interest that depend on the solution of a partial differential equation and optimal control problems having random inputs, e.g., coefficients, boundary data, source term, etc. Monte Carlo methods are the most used approach used for this purpose. We discuss other approaches that, in some settings, incur far less computational costs. These include quasi-Monte Carlo, polynomial chaos, stochastic collocation, compressed sensing, reduced-order modeling.