用机器学习按函数高度分层，提升蒙特卡洛模拟精度
LeStrat-Net: Lebesgue style stratification for Monte Carlo simulations powered by machine learning
- 基于勒贝格积分思想，按函数值高度划分采样区域
- 神经网络预判复杂分界，实现高维空间高效分层
- 适用于需要降方差的物理模拟与事件筛选任务
我们提出一种机器学习算法，用于改进蒙特卡洛采样中的分层策略。该方法借鉴勒贝格积分思想，依据被积函数的取值高度划分定义域，使等高线决定区域形状，可适应任意复杂函数行为。利用神经网络强大的函数拟合能力，预先学习并预测这些复杂分界，对大规模定义域样本进行预分类。基于此预分类结果，可选取所需数量的采样点，用于方差降低、积分计算乃至事件选择。网络最终不仅定义各区域边界，还负责计算每个区域的多维体积。
原文摘要 · Abstract (English)
We develop a machine learning algorithm to turn around stratification in Monte Carlo sampling. We use a different way to divide the domain space of the integrand, based on the height of the function being sampled, similar to what is done in Lebesgue integration. This means that isocontours of the function define regions that can have any shape depending on the behavior of the function. We take advantage of the capacity of neural networks to learn complicated functions in order to predict these complicated divisions and preclassify large samples of the domain space. From this preclassification we can select the required number of points to perform a number of tasks such as variance reduction, integration and even event selection. The network ultimately defines the regions with what it learned and is also used to calculate the multi-dimensional volume of each region.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。