cuVegas：通过基于CUDA的VEGAS增强算法并行实现加速多维蒙特卡洛积分
cuVegas: Accelerate Multidimensional Monte Carlo Integration through a Parallelized CUDA-based Implementation of the VEGAS Enhanced Algorithm
AI总结：
本研究提出基于CUDA的VEGAS+算法实现cuVegas，优化GPU多维积分的工作负载分配，相比CPU实现提速2-3个数量级，比现有最优GPU实现快2倍。
摘要：
本文介绍了cuVegas，这是一种基于CUDA的Vegas增强算法（VEGAS+）实现，针对GPU环境下的多维积分进行了优化。VEGAS+算法是蒙特卡洛积分的一种高级形式，以其在处理复杂高维被积函数时的适应性和有效性著称。它结合了多种方差缩减技术，即自适应重要性采样和一种自适应分层采样的变体，这使其特别擅长处理具有多个峰值的被积函数，或是与积分体积对角线对齐的被积函数。作为一种蒙特卡洛积分方法，该任务非常适合并行化和GPU执行。我们的实现cuVegas旨在利用GPU固有的并行性，解决标准实现中通常会影响效率的工作负载分配难题。我们对cuVegas与现有的CPU和GPU实现进行了全面分析，结果表明其性能提升显著：相较于CPU实现提升了2到3个数量级，相较于现有最优GPU实现提升了2倍。我们还展示了针对VEGAS+设计的被积函数的加速效果，这类被积函数具有多个峰值或其他与积分体积对角线对齐的显著结构。
英文摘要：
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.
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