CONSTRUCTING DIMENSION-ADAPTIVE SPARSE GRID INTERPOLANTS USING PARALLEL FUNCTION EVALUATIONS

2006 ◽  
Vol 16 (04) ◽  
pp. 407-418
Author(s):  
ANDREAS KLIMKE ◽  
BARBARA WOHLMUTH
Keyword(s):  
Adaptive Algorithm ◽  
Sparse Grid ◽  
High Dimensional ◽  
Parallel Efficiency ◽  
Standard Algorithm ◽  
Grid Algorithm ◽  
Surrogate Functions ◽  
Time Required ◽  
Grid Interpolation

Dimension-adaptive sparse grid interpolation is a powerful tool to obtain surrogate functions of smooth, medium to high-dimensional objective models. In case of expensive models, the efficiency of the sparse grid algorithm is governed by the time required for the function evaluations. In this paper, we first briefly analyze the inherent parallelism of the standard dimension-adaptive algorithm. Then, we present an enhanced version of the standard algorithm that permits, in each step of the algorithm, a specified number (equal to the number of desired processes) of function evaluations to be executed in parallel, thereby increasing the parallel efficiency.

scholarly journals A Hyperspherical Adaptive Sparse-Grid Method for High-Dimensional Discontinuity Detection

2015 ◽  
Vol 53 (3) ◽  
pp. 1508-1536 ◽  
Author(s):  
G. Zhang ◽  
C. Webster ◽  
M. Gunzburger ◽  
J. Burkardt
Keyword(s):  
Grid Method ◽  
Sparse Grid ◽  
High Dimensional ◽  
Discontinuity Detection ◽  
Sparse Grid Method

An adaptive algorithm for high‐dimensional integrals on heterogeneous CPU‐GPU systems

2018 ◽  
Vol 31 (19) ◽  
Author(s):  
Giuliano Laccetti ◽  
Marco Lapegna ◽  
Valeria Mele ◽  
Raffaele Montella
Keyword(s):  
Adaptive Algorithm ◽  
High Dimensional

scholarly journals Parallelisation of sparse grids for large scale data analysis

2006 ◽  
Vol 48 (1) ◽  
pp. 11-22 ◽  
Author(s):  
Jochen Garcke ◽  
Markus Hegland ◽  
Ole Nielsen
Keyword(s):  
Large Scale ◽  
Predictive Modelling ◽  
Sparse Grids ◽  
Sparse Grid ◽  
High Dimensional ◽  
Combination Technique ◽  
Parallel Solvers ◽  
Regular Grids ◽  
Timing Model ◽  
Dimensional Approximation

AbstractSparse grids 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 sparse grid combination technique prescribes how approximations on a collection of anisotropic grids can be combined to approximate high dimensional functions.In this paper we study the parallelisation of fitting data onto a sparse grid. The computation can be done entirely by fitting partial models on a collection of regular grids. This allows parallelism over the collection of 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. Using a simple timing model we confirm that the most effective methods are obtained when both types of parallelism are used.

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