Related papers: Explainable AI-assisted Optimization for Feynman I…
The Feynman path integral formalism has inspired the development of memory-efficient and parallelizable classical algorithms for simulating quantum computers. We adapt this approach for the calculation of probability amplitudes of…
The reduction of Feynman integrals to a basis of linearly independent master integrals is a pivotal step in loop calculations, but also one of the main bottlenecks. In this paper, we assess the impact of using transverse integration…
We revisit the idea of numerically integrating the differential form of Feynman integrals. With a novel approach for the treatment of branch cuts, we develop an integrator capable of evaluating a basis of master integrals in double and…
An algorithm for the reduction of massive Feynman integrals with any number of loops and external momenta to a minimal set of basic integrals is proposed. The method is based on the new algorithm for evaluating tensor integrals,…
In the computation of Feynman integrals which evaluate to multiple polylogarithms one encounters quite often square roots. To express the Feynman integral in terms of multiple polylogarithms, one seeks a transformation of variables, which…
We invent an automated method for computing the divergent part of Feynman integrals in dimensional regularization. Our method exploits simplifications from four-dimensional integration-by-parts identities. Leveraging algorithms from the…
Standard integration-by-parts (IBP) reduction methods typically yield Feynman integral bases where the reduction of some integrals gives rise to coefficients singular as the dimensional regulator $\epsilon\rightarrow 0$. These singular…
While Bayesian neural networks (BNNs) have drawn increasing attention, their posterior inference remains challenging, due to the high-dimensional and over-parameterized nature. To address this issue, several highly flexible and scalable…
FIRE7 is a major update to the FIRE program for integration-by-parts (IBP) reduction of Feynman integrals. A large part of improvements is related to the automatic reduction and reconstruction with the modular arithmetic approach, while the…
We present a detailed description of the recent idea for a direct decomposition of Feynman integrals onto a basis of master integrals by projections, as well as a direct derivation of the differential equations satisfied by the master…
In this article, we present the package {\tt Blade} as the first implementation of the block-triangular form improved Feynman integral reduction method. The block-triangular form has orders of magnitude fewer equations compared to the plain…
Bayesian optimal experimental design has immense potential to inform the collection of data so as to subsequently enhance our understanding of a variety of processes. However, a major impediment is the difficulty in evaluating optimal…
We introduce a machine-learning framework based on symbolic regression to extract the full symbol alphabet of multi-loop Feynman integrals. By targeting the analytic structure rather than reduction, the method is broadly applicable and…
We investigate the reduction of Feynman integrals to master integrals using Gr\"obner bases in a rational double-shift algebra Y in which the integration-by-parts (IBP) relations form a left ideal. The problem of reducing a given family of…
We motivate the use of quantum algorithms in particle physics and provide a brief overview of the most recent applications at high-energy colliders. In particular, we discuss in detail how a quantum approach reduces the complexity of jet…
We present an improved method for symbolic regression that seeks to fit data to formulas that are Pareto-optimal, in the sense of having the best accuracy for a given complexity. It improves on the previous state-of-the-art by typically…
Negative dimensional integration method (NDIM) is revealing itself as a very useful technique for computing Feynman integrals, massless and/or massive, covariant and non-covariant alike. Up to now, however, the illustrative calculations…
We suggest a mathematical definition of the notion of master integrals and present a brief review of algorithmic methods to solve reduction problems for Feynman integrals based on integration by parts relations. In particular, we discuss a…
This work investigates in detail the performance and advantages of a new quantum Monte Carlo integrator, dubbed Quantum Fourier Iterative Amplitude Estimation (QFIAE), to numerically evaluate for the first time loop Feynman integrals in a…
The design of informatively rich input signals is essential for accurate system identification, yet classical Fisher-information-based methods are inherently local and often inadequate in the presence of significant model uncertainty and…