Global Sensitivity Analysis on Numerical Input Parameters with Application to Cyclotrons

by Mr Matthias Frey

Thursday 19 Sept 2019, 14:00 → 15:00 Europe/Zurich

OHSA/B17 (Paul Scherrer Institut)

Every computer model depends on numerical input parameters that are chosen according to mostly conservative but rigorous numerical or empirical estimates. These parameters could for example be the step size for time integrators, a seed for pseudo-random number generators, a threshold or the number of grid points to discretize a computational domain. In case a numerical model is enhanced with new algorithms and modelling techniques the numerical influence on the quantities of interest, the running time as well as the accuracy is often initially unknown.

Parameters might therefore be chosen too conservatively which keeps the cost per simulation unnecessarily high and wastes computing resources. Hence, it is essential to identify the most critical numerical parameters and to analyze their effect on the result in order to minimize the time-to-solution without losing significantly on accuracy. Surrogate models based on polynomial chaos expansion allow the evaluation of sensitivities based on Sobol's indices. Nevertheless, many numerical parameters, such as the number of levels in adaptive mesh refinement (AMR), are restricted to integer values and exhibit a small range which is why the sampling hyperspace is anisotropic.

In this presentation, we present the first results of a global sensitivity analysis that will help to reduce computational complexity of further numerical studies of neighbouring bunch simulations in high-intensity cyclotrons.