Related papers: Targeting Multi-Loop Integrals with Neural Network…
Feynman integral reduction based on intersection theory provides an alternative to the traditional integration-by-parts method, yet its practical application has been constrained by the large number of variables required in the computation.…
This paper discusses a new method to solve definite integrals using artificial neural networks. The objective is to build a neural network that would be a novel alternative to pre-established numerical methods and with the help of a…
In the very near future the first data from LHC will be available. The searches for the Higgs boson and for new physics will require precise predictions both for the signal and the background processes. Tree level calculations typically…
Microlensing light curves are typically computed either by ray-shooting maps or by contour integration via Green's theorem. We present an improved version of the second method that includes a parabolic correction in Green's line integral.…
The numerical unitarity approach has been important for obtaining reliable QCD predictions for the LHC. Here I discuss the extension of the approach beyond the leading quantum corrections for computing multi-loop amplitudes. The numerical…
Mixed-precision Deep Neural Networks achieve the energy efficiency and throughput needed for hardware deployment, particularly when the resources are limited, without sacrificing accuracy. However, the optimal per-layer bit precision that…
Monte Carlo methods are widely used in particle physics to integrate and sample probability distributions (differential cross sections or decay rates) on multi-dimensional phase spaces. We present a Neural Network (NN) algorithm optimized…
Finite element methods usually construct basis functions and quadrature rules for multidimensional domains via tensor products of one-dimensional counterparts. While straightforward, this approach results in integration spaces larger than…
In recent times, an increasing number of researchers have been devoted to utilizing deep neural networks for end-to-end flight navigation. This approach has gained traction due to its ability to bridge the gap between perception and…
We address the problem of improving the performance and in particular the sample complexity of deep neural networks by enforcing and guaranteeing invariances to symmetry transformations rather than learning them from data. Group-equivariant…
Multi-loop scattering amplitudes constitute a serious bottleneck in current high-energy physics computations. Obtaining new integrand level representations with smooth behaviour is crucial for solving this issue, and surpassing the…
We propose a novel multi-dimensional integration algorithm using a machine learning (ML) technique. After training a ML regression model to mimic a target integrand, the regression model is used to evaluate an approximation of the integral.…
We numerically integrate finite two- and three-loop scalar integrals using the threshold subtraction method. This represents a first step towards extending our calculation of the $N_f$-part to the full NNLO virtual corrections for the…
Using integration by parts relations, Feynman integrals can be represented in terms of coupled systems of differential equations. In the following we suppose that the unknown Feynman integrals can be given in power series representations,…
We present a historiographical review of algorithms and computer codes developed for solving integration-by-parts relations for Feynman integrals. This procedure is one of the key steps in the evaluation of Feynman integrals, since it…
We present a method to accelerate the numerical evaluation of spatial integrals of Feynman diagrams when expressed on the real frequency axis. This can be realized through use of a renormalized perturbation expansion with a constant but…
We present a geometric multilevel optimization approach that smoothly incorporates box constraints. Given a box constrained optimization problem, we consider a hierarchy of models with varying discretization levels. Finer models are…
Behavior of neural networks is irremediably determined by the specific loss and data used during training. However it is often desirable to tune the model at inference time based on external factors such as preferences of the user or…
The method for functional reduction of Feynman integrals, proposed by the author, is used to calculate one-loop integrals corresponding to diagrams with four external lines. The integrals that emerge from amplitudes for the scattering of…
We introduce an algebro-geometrically motived integration-by-parts (IBP) reduction method for multi-loop and multi-scale Feynman integrals, using a framework for massively parallel computations in computer algebra. This framework combines…