LeStrat-Net: Lebesgue style stratification for Monte Carlo simulations powered by machine learning

TL;DR

This paper introduces LeStrat-Net, a machine learning-based stratification method for Monte Carlo simulations that uses neural networks to adaptively partition the domain based on the function's height, improving variance reduction and integration accuracy.

Contribution

It proposes a novel neural network approach to Lebesgue-style domain stratification, enabling flexible, shape-adaptive regions for Monte Carlo sampling.

Findings

Enhanced variance reduction in Monte Carlo simulations.

Flexible domain partitioning based on function behavior.

Improved accuracy in multi-dimensional integration.

Abstract

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.