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Fast Adaptive Sampling Technique for Multi-Dimensional Integral Estimation Using GPUs

Pradeep Rao, Sayantan Mitra, Foy Nathanael, G. N. Srinivasa Prasanna
Infosys Limited, Bangalore, India
Nvidia GPU Technology Conference, 2012

@article{rao2012fast,

   title={FAST ADAPTIVE SAMPLING TECHNIQUE FOR MULTI-DIMENSIONAL INTEGRAL ESTIMATION USING GPUS},

   author={Rao, P. and Nathana{"e}l, F. and Mitra, S. and Prasanna, G.N.S.},

   year={2012}

}

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Evaluating multi-dimensional integrals is a commonly encountered problem in many areas of science including Physics and Volume estimation of convex bodies. One of the widely used techniques for integral evaluation in large dimensions is the Monte Carlo method. Vanilla Monte Carlo methods of Integral Estimation use uniform sampling techniques. Variance of such uniform sampling reduces as 1/vSample-size, which is too slow for most real life applications. In this study, we discuss about an adaptive sampling technique called VEGAS which reduces the variance at a much faster rate than uniform sampling. We present a new parallel implementation for VEGAS based on CUDA that can significantly reduce the computation time of multidimensional integrals. We show that our GPU based implementation of VEGAS achieves up to a 45x speed up over an equivalent CPU based implementation.
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