ZMCintegral: Python Package for Monte Carlo Integration on Multi-GPU Devices

ZMCintegral is an easy-to-use Python package designed for Monte Carlo integration on multi-GPU devices. It offers features such as random sampling within a domain, adaptive importance sampling using methods like Vegas, and leveraging TensorFlow-GPU backend for efficient computation. The package provides a powerful solution for integrating complex functions, with a focus on stability and performance.

• Monte Carlo Integration
• Python Package
• Multi-GPU Devices
• Adaptive Sampling
• TensorFlow

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1. https://github.com/Letianwu/ZMCintegral ZMCintegral ---an easy to Use Python Package for Monte Carlo Integration on Multi-GPU Devices WU Hongzhong, ZHANG Junjie, PANG Longgang, WANG Qun To appear soon 2024/9/29 zjacob@mail.ustc.edu.cn 1

2. Random Sampling within a Domain ?(?1) ?(?) ?(?2) ?(?3) + ?(??) ?? ? ? ?? (?? ??)1 3 ?(??) ?? ?? ?? ? 2024/9/29 zjacob@mail.ustc.edu.cn 2

3. Random Sampling within a Domain Uniform sampling is sufficient for stable domain regions. 1 ?. The convergence slowly follows Ineffective for multi-dimensional, rapid oscillating or high peaking functions. Details of the integrands would be difficult to extract. 2024/9/29 zjacob@mail.ustc.edu.cn 3

4. Adaptive Importance Sampling: Vegas as an example Vegas, adaptively adjusts the number of points in each grid domain such that more points would be evaluated for anxious domains. ?(?) ? 2024/9/29 zjacob@mail.ustc.edu.cn 4

5. Adaptive Importance Sampling: ZMCintegral with Tensorflow-GPU backend ZMCintegral amplifies the anxious domains iteratively, and with the benefit of GPU, it samples a huge amount of points in each domain with a heuristic tree search. Very easy to use Huge amount (1,000,000,000) of points for each anxious domain ?(?) ? 2024/9/29 zjacob@mail.ustc.edu.cn 5

6. 10 Result: ZMCintegral VS VEGAS sin[?1 + ?2 + ?3 + ?4 + ?5 + ?6]??1??2??3??4??5??6 0 2024/9/29 zjacob@mail.ustc.edu.cn 6

7. Thank you ZHANG Junjie 2024/9/29 zjacob@mail.ustc.edu.cn 7