i-flow: High-dimensional Integration and Sampling with Normalizing Flows

Abstract

In many fields of science, high-dimensional integration is required. Numerical methods have been developed to evaluate these complex integrals. We introduce the code i-flow, a python package that performs high-dimensional numerical integration utilizing normalizing flows. Normalizing flows are machine-learned, bijective mappings between two distributions. i-flow can also be used to sample random points according to complicated distributions in high dimensions. We compare i-flow to other algorithms for high-dimensional numerical integration and show that i-flow outperforms them for high dimensional correlated integrals.

Measuring QCD Splittings with Invertible Networks

“…Technically, our BayesFlow approach [47] is based on the conditional version [48,49] of invertible networks (INNs) [50][51][52], a specific realization of normalizing flows [53][54][55][56]. These networks have been studied in relation to phase space generation [57][58][59][60], event generation [61], anomaly detection [62], detector and parton shower unfolding [63], and density estimation [64]. We will introduce our QCD inference framework in Sec.…”

Uncertainties associated with GAN-generated datasets in high energy physics

“…• We would like to point out that our argument is not pertinent to parton-level ML-based generative approaches which learn directly from an oracle which can be queried for the underlying true distribution (matrix-element), instead of learning from data generated under that distribution [34][35][36][37][38][39][40].…”

Annealed Flow Transport Monte Carlo

“…This approach has been investigated in many recent work; see e.g. Gao et al (2020); Noé et al (2019); Wirnsberger et al (2020). Although it is attractive, it is also well-known that optimizing this 'mode-seeking' KL can lead to an approximation of the target T # π 0 which has thinner tails than the target π and ignore some of its modes; see e.g.…”