Parallelisation of Sparse Grids for Large Scale Data Analysis

Sparse Grids (SG), due to Zenger, are the basis for efficient high dimensional approximation and have recently been applied successfully to predictive modelling. They are spanned by a collection of simpler function spaces represented by regular grids. The combination technique prescribes how approximations on simple grids can be combined to approximate the high dimensional functions. It can be improved by iterative refinement. Fitting sparse grids admits the exploitation of parallelism at various stages. The fit can be done entirely by fitting partial models on regular grids. This allows parallelism over the partial grids. In addition, each of the partial grid fits can be parallelised as well, both in the assembly phase where parallelism is done over the data and in the solution stage using traditional parallel solvers for the resulting PDEs. A simple timing model confirms that the most effective methods are obtained when both types of parallelism are used. AMS subject classification. 62H30, 65D10, 68Q22