Targeting multi-loop integrals with neural networks

Abstract

Numerical evaluations of Feynman integrals often proceed via a deformation of the integration contour into the complex plane. While valid contours are easy to construct, the numerical precision for a multi-loop integral can depend critically on the chosen contour. We present methods to optimize this contour using a combination of optimized, global complex shifts and a normalizing flow. They can lead to a significant gain in precision.

Ephemeral Learning - Augmenting Triggers with Online-Trained Normalizing Flows

“…This allows us to train our ONLINEFLOW without stopping criterion, a property well suited for training online. Furthermore, NFs have been shown to precisely learn complex distributions in particle physics [32][33][34][35][36][37][38][39][40][41][42]. The statistical benefits of using generative models are discussed in Ref.…”

Modeling hadronization using machine learning

“…This model requires extra parameters to describe the hadrons' transverse momenta and heavy particle suppression, and has some challenges describing baryon production. Over O (20) parameters are required by the string model to describe the hadronization.…”

“…Such ML models could be directly built from data and provide insights into the current phenomenological models. While ML techniques have recently entered into the development of event generators, through adaptive integration [15][16][17][18][19][20], parton showers [21][22][23][24][25][26][27][28][29], ML based fast detector or event simulations , and model parameter tuning [56,57], the application of ML to the problem of hadronization as the final step in the Monte Carlo pipeline is entirely new, to the best of our knowledge. The present manuscript represents the first step toward building a full-fledged ML based hadronization framework.…”

Event Generation and Density Estimation with Surjective Normalizing Flows

“…Of these models, normalizing flows have the particular advantage of simultaneously enabling event generation and likelihood evaluation, the latter of which is useful in other applications. As a result, they have been successfully used for a variety of tasks including event generation [8][9][10][11][12][13][14][15][16][17][18][19][20], anomaly detection [21][22][23], unfolding [24], the calculation of loop integrals [25], and likelihood-free inference [26][27][28].…”