I- flow: High-dimensional integration and sampling with normalizing flows

Christina Gao,Claudius Krause,Joshua Isaacson

doi:10.1088/2632-2153/abab62

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. The i-flow code is publicly available on gitlab at https://gitlab.com/i-flow/i-flow.

Highlights

Simulation based on first principles is an important practice, because it is the only way that a theoretical model can be checked against experiments or real-world data
In high-energy physics (HEP) experiments, a thorough understanding of the properties of known physics forms the basis of any searches that look for new effects
We show in Sec III A that at most 2 log2 D number of Coupling Layers are required in order to express non-separable structures of the integrand

Summary

Introduction

Simulation based on first principles is an important practice, because it is the only way that a theoretical model can be checked against experiments or real-world data. In high-energy physics (HEP) experiments, a thorough understanding of the properties of known physics forms the basis of any searches that look for new effects. This can only be achieved by an accurate simulation, which in many cases boils down to performing an integral and sampling from it. Monte-Carlo (MC) methods still remain as the most important techniques for solving high-dimensional problems across many fields, including for instance: biology [1, 2], chemistry [3], astronomy [4], medical physics [5], finance [6] and image rendering [7]. The extraordinary performance of the experiments requires an amount of simulated data that soon cannot be delivered with current algorithms and computational resources [10, 11]

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