From a simulation, we expect to obtain useful and reliable information. Therefore, it has to be carefully designed. Nevertheless, each simulation involves errors which are usually categorized into three types: (1) Due to simplification of the physics the so-called model error is introduced. (2) We need some sort of discretization to work with the model and that introduces numerical errors. Finally, (3) the simulation requires input data that is usually incomplete, has low accuracy, or is simply wrong. Uncertainty quantification deals with quantifying the error that is introduced by data, typically for large-scale (and, thus, expensive) simulations. One can distinguish between Monte Carlo, projection-based (stochastic Galerkin), and interpolation (collocation) methods.
There is a wide range of student projects available. They reach from applying these methods to current problems and codes, to adapting and developing new approaches for particular problem classes.