Efficient Solution of Ordinary Differential Equations with High-Dimensional Parametrized Uncertainty (Communications in Computational Physics, 2011)
The important task of evaluating the impact of random parameters on theoutput of stochastic ordinary differential equations (SODE) can be computationallyvery demanding, in particular for problems with a high-dimensional parameter space.In this work we consider this problem in some detail and demonstrate that by combiningseveral techniques one can dramatically reduce the overall cost without impactingthe predictive accuracy of the output of interests. We discuss how the combination ofANOVA expansions, different sparse grid techniques, and the total sensitivity index(TSI) as a pre-selective mechanism enables the modeling of problems with hundreds ofparameters. We demonstrate the accuracy and efficiency of this approach on a numberof challenging test cases drawn from engineering and science.