cuVegas: Accelerate Multidimensional Monte Carlo Integration through a Parallelized CUDA-based Implementation of the VEGAS Enhanced Algorithm

TL;DR

cuVegas is a GPU-accelerated implementation of the VEGAS+ Monte Carlo integration algorithm, significantly improving performance for high-dimensional integrals with complex structures by leveraging parallel computing.

Contribution

This work introduces cuVegas, a novel CUDA-based implementation of VEGAS+ that enhances multi-dimensional Monte Carlo integration efficiency on GPUs.

Findings

Achieves 100-1000x speedup over CPU implementations.

Doubles the performance of existing GPU implementations.

Effectively handles integrands with multiple peaks and diagonal structures.

Abstract

This paper introduces cuVegas, a CUDA-based implementation of the Vegas Enhanced Algorithm (VEGAS+), optimized for multi-dimensional integration in GPU environments. The VEGAS+ algorithm is an advanced form of Monte Carlo integration, recognized for its adaptability and effectiveness in handling complex, high-dimensional integrands. It employs a combination of variance reduction techniques, namely adaptive importance sampling and a variant of adaptive stratified sampling, that make it particularly adept at managing integrands with multiple peaks or those aligned with the diagonals of the integration volume. Being a Monte Carlo integration method, the task is well suited for parallelization and for GPU execution. Our implementation, cuVegas, aims to harness the inherent parallelism of GPUs, addressing the challenge of workload distribution that often hampers efficiency in standard implementations. We present a comprehensive analysis comparing cuVegas with existing CPU and GPU implementations, demonstrating significant performance improvements, from two to three orders of magnitude on CPUs, and from a factor of two on GPUs over the best existing implementation. We also demonstrate the speedup for integrands for which VEGAS+ was designed, with multiple peaks or other significant structures aligned with diagonals of the integration volume.