ZMCintegral: Python Package for Monte Carlo Integration on Multi-GPU Devices
WU Hongzhong, ZHANG Junjie, PANG Longgang, WANG Qun
WU Hongzhong, ZHANG Junjie, PANG Longgang, WANG Qun
ZMCintegral
ZMCintegral
---an easy to Use Python Package
---an easy to Use Python Package
for Monte Carlo Integration on Multi-GPU
for Monte Carlo Integration on Multi-GPU
Devices
Devices
2024/9/29
zjacob@mail.ustc.edu.cn
1
To appear soon …
To appear soon …
https://github.com/Letianwu/ZMCintegral
https://github.com/Letianwu/ZMCintegral
2024/9/29
zjacob@mail.ustc.edu.cn
2
Random Sampling within a Domain
Random Sampling within a Domain
2024/9/29
zjacob@mail.ustc.edu.cn
3
Random Sampling within a Domain
Random Sampling within a Domain
Uniform sampling is sufficient for “stable” domain regions.
Uniform sampling is sufficient for “stable” domain regions.
Ineffective for multi-dimensional, rapid oscillating or high
Ineffective for multi-dimensional, rapid oscillating or high
peaking functions.
peaking functions.
Details of the integrands would be difficult to extract.
Details of the integrands would be difficult to extract.
2024/9/29
zjacob@mail.ustc.edu.cn
Adaptive Importance Sampling: Vegas as an example
Adaptive Importance Sampling: Vegas as an example
Vegas, adaptively adjusts the number of points
Vegas, adaptively adjusts the number of points
in each grid domain such that more points
in each grid domain such that more points
would be evaluated for anxious domains.
would be evaluated for anxious domains.
4
Adaptive Importance Sampling: ZMCintegral with Tensorflow-GPU backend
Adaptive Importance Sampling: ZMCintegral with Tensorflow-GPU backend
ZMCintegral amplifies the anxious domains iteratively, and with the
ZMCintegral amplifies the anxious domains iteratively, and with the
benefit of GPU, it samples a huge amount of points in each domain
benefit of GPU, it samples a huge amount of points in each domain
，
，
with
with
a heuristic tree search.
a heuristic tree search.
Very easy to use
Very easy to use
Huge amount (1,000,000,000) of
Huge amount (1,000,000,000) of
points for each anxious domain
points for each anxious domain
2024/9/29
zjacob@mail.ustc.edu.cn
5
Result: ZMCintegral VS VEGAS
Result: ZMCintegral VS VEGAS
2024/9/29
zjacob@mail.ustc.edu.cn
6
ZHANG Junjie
ZHANG Junjie
Thank you
Thank you
2024/9/29
zjacob@mail.ustc.edu.cn
7
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.
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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
Random Sampling within a Domain ?(?1) ?(?) ?(?2) ?(?3) + ?(??) ?? ? ? ?? (?? ??)1 3 ?(??) ?? ?? ?? ? 2024/9/29 zjacob@mail.ustc.edu.cn 2
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
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
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
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
Thank you ZHANG Junjie 2024/9/29 zjacob@mail.ustc.edu.cn 7
