ZMCintegral: a Package for Multi-Dimensional Monte Carlo Integration on Multi-GPUs

Abstract

We have developed a Python package ZMCintegral for multi-dimensional Monte Carlo integration on multiple Graphics Processing Units(GPUs). The package employs a stratified sampling and heuristic tree search algorithm. We have built three versions of this package: one with Tensorflow and other two with Numba, and both support general user defined functions with a user-friendly interface. We have demonstrated that Tensorflow and Numba help inexperienced scientific researchers to parallelize their programs on multiple GPUs with little work. The precision and speed of our package is compared with that of VEGAS for two typical integrands, a 6-dimensional oscillating function and a 9-dimensional Gaussian function. The results show that the speed of ZMCintegral is comparable to that of the VEGAS with a given precision. For heavy calculations, the algorithm can be scaled on distributed clusters of GPUs.

arXiv comment18 pages, 9 figures

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• Impact of initial fluctuations and nuclear deformations in isobar collisions
• ZMCintegral-v5: Support for Integrations with the Scanning of Large Parameter Grids on Multi-GPUs
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• JefiGPU: Jefimenko's Equations on GPU
• Recent developments in chiral and spin polarization effects in heavy-ion collisions
• Many-gluon tree amplitudes on modern GPUs: A case study for novel event generators
• Row-clustering of a Point Process-valued Matrix
• Nuclear deformation effects in photoproduction of $\rho$ mesons in ultraperipheral isobaric collisions
• ZMCintegral-v5.1: Support for Multi-function Integrations on GPUs
• Lepton pair production in ultra-peripheral collisions