Efficiency improvements by code Intrinsic uncertainty quantification via Monte Carlo methods

In view of the stagnating computing power per core, this project aims at improving the computational efficiency of uncertainty quantification (UQ) methodologies applied to deterministic simulation codes. This will be done by developing a methodology to implement code intrinsic UQ. The core of this methodology will be to extend variables, holding uncertain input parameters, by a stochastic dimension. The propagation of these variables through the code, as well as their potential interference with each other along the propagation path, will then be analysed. From this approach it is first of all expected to gain higher computational efficiency due to higher data density in inner, computationally intensive kernels. In other words, the approach will exploit the hardware features of modern CPUs more efficiently as x86_64 CPUs are e.g. designed to deal with so called dense kernels which do not make use of indirect addressing of data. Second of all, it is expected to gain additional efficiency by saving random experiments in UQ Methods by analysing the variables' interactions and with those potential convolutions of their statistical distributions. The technical approach will be to first develop a code analysis methodology based on established tools and apply it to two different simulation codes. One will be the FLEXI CFD code developed by the group of Claus-Dieter Munz. The other one will be an HLRS in house FEM implementation. Starting from these analyses the technical aspects of efficiency improvements within the code will be linked to the theoretical aspects of stochastic of partial differential equations (PDEs). Based on these findings, possibilities for the generalizations of the complete methodology, in form of compiler or high-level language extensions, will be evaluated.