Udo von Toussaint - Max Planck Institute for Plasma Physics
Almost all simulation codes depend on a large number of input parameters. However, many of these parameters are uncertain and a proper comparison with experimental data or other models requires the quantification of the uncertainty of the result. Unfortunately, the computational demand of single simulation runs often severely restricts the quantification of output uncertainties by full-grid or simple sampling (eg. Monte Carlo sampling) based approaches due to the curse of dimensionality for more than a very limited number of uncertain input parameters. To reduce the computational effort we utilized the non-intrusive reduced-order model approach (polynomial chaos expansion), which not only reduces the number of function evaluations but provides simultaneously a quantitative measure which combinations of inputs have the most important impact on the result, ie. it yields a sensitivity analysis and the associated Sobol coefficients. The proposed method is applied to SDTRIM-simulations with several uncertain and Gaussian distributed input parameters (ie. impact angle, projectile energy, surface binding energy) and the results are compared to full-grid based approaches and sampling based methods with respect to reliability, efficiency and scalability. Furthermore we outline recent developments towards high-dimensional problems.