A Nonintrusive POD Approach for High Dimensional Problems using Sparse Grids

Abstract

Reduced order models are effective in reducing the computational burden of large-scale complex systems. Proper Orthogonal Decomposition (POD) is one of the most important methods for such application. Nevertheless, problems parametrized on high dimensional spaces require computations of an enormous number of simulations in the offline phase. In this paper, the use of sparse grids is suggested to select the sampling points in an efficient manner. The method exploits the hierarchical nature of the Smolyak algorithm to select the sparse grid level based on the singular values of the POD basis. Then, a nonintrusive reduced order model is built using Smolyak’s combination technique. The proposed method was tested and compared with Radial Basis Functions in two nuclear applications. The first was a one-dimensional slab solved as a diffusion eigenvalue problem and the second was the two-dimensional IAEA benchmark problem. In both cases, the results showed that while Radial Basis Functions resulted in a faster reduced order model, Smolyak’s model provided superior accuracy.