Abstract
The generation of accurate neutrino-nucleus cross section models needed for neutrino oscillation experiments requires simultaneously the description of many degrees of freedom and precise calculations to model nuclear responses. The detailed calculation of complete models makes the Monte Carlo generators slow and impractical. We present exhaustive neural importance sampling, a method based on normalizing flows to find a suitable proposal density for rejection sampling automatically and efficiently, and discuss how this technique solves common issues of the rejection algorithm.
Highlights
We further explore the possibility of utilizing normalizing flows to find a proposal function for a given target density to perform rejection sampling for Monte Carlo (MC) samples, and analyze its viability through the following points: (i) We discuss the importance of adding an additional density to the target one to assure the coverage of the whole phase space when performing rejection sampling
We have presented exhaustive neural importance sampling (ENIS), a framework to find accurate proposal density functions in the form of normalizing flows
This proposal density is subsequently used to perform rejection sampling on a target density to obtain MC data sets or compute expected values
Summary
In modern science and engineering disciplines, the generation of random samples from a probability density function to obtain data sets or compute expectation values has become an essential tool These theoretical models can be described by a target probability density function pðxÞ. A standard numerical method to obtain such data set is to perform a Markov Chain Monte Carlo (MCMC) algorithm [1], which provides good results for expected value calculations. (3) The sampling efficiency decreases rapidly with the number of dimensions To avoid these inconveniences, one would like to have a method to find a proposal function that adapts to a given target density automatically. We further explore the possibility of utilizing normalizing flows to find a proposal function for a given target density to perform rejection sampling for MC samples, and analyze its viability through the following points:. The technique may help model developers extract expected values from their theoretical predictions in realistic conditions by including simple detector effects in models, such as effects of detector acceptance cuts, impact of model degrees of freedom on the predictions, or uncertainty propagation
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