Related papers: Uncovering Singularities in Feynman Integrals via …

In this paper, we explore the recursive structure of Baikov representations for Feynman integrals. We demonstrate that the various Baikov representations for all sectors of an integral family can be organized in a tree-like structure. Using…

We show how studying leading singularities of Feynman diagrams, when all momenta are complex, gives a simple way of writing multi-loop and multi-particle scattering amplitudes in N=4 super Yang-Mills. The simplicity of the method is…

Modeling real-world systems requires accounting for noise - whether it arises from unpredictable fluctuations in financial markets, irregular rhythms in biological systems, or environmental variability in ecosystems. While the behavior of…

Logic-based machine learning aims to learn general, interpretable knowledge in a data-efficient manner. However, labelled data must be specified in a structured logical form. To address this limitation, we propose a neural-symbolic learning…

We introduce SymbolFit, a framework that automates parametric modeling by using symbolic regression to perform a machine-search for functions that fit the data while simultaneously providing uncertainty estimates in a single run.…

It could be challenging for students and instructors to piece together a different regression concepts to coherently perform a complete data analysis. I propose using a framework which reinforces the detailed steps towards regression in…

This paper presents an automated approach for interpretable feature recommendation for solving signal data analytics problems. The method has been tested by performing experiments on datasets in the domain of prognostics where…

We introduce a symbolic method for the evaluation of definite integrals containing combinations of various functions, including exponentials, logarithm and products of Bessel functions of different types. The method we develop is naturally…

Feynman integrals obey linear relations governed by intersection numbers, which act as scalar products between vector spaces. We present a general algorithm for constructing multivariate intersection numbers relevant to Feynman integrals,…

We present an interesting study of Feynman integral reduction that does not employ integration-by-parts identities. Our approach proceeds by studying the equivalence relations of integral contours in the Feynman parameterization. We find…

Two-loop corrections to scattering amplitudes are crucial theoretical input for collider physics. Recent years have seen tremendous advances in computing Feynman integrals, scattering amplitudes, and cross sections for five-particle…

Recently a nice work about the understanding of one-loop integrals has been done in [1] using the tricks of the projective space language associated to their Feynman parametrization. We find this language is also very suitable to deal with…

We present a novel technique for the analytic evaluation of multifold Mellin-Barnes (MB) integrals, which commonly appear in physics, as for instance in the calculations of multi-loop multi-scale Feynman integrals. Our approach is based on…

In this paper we introduce an active learning method for symbolic regression using StackGP. The approach begins with a small number of data points for StackGP to model. To improve the model the system incrementally adds a data point such…

In a regression task, a function is learned from labeled data to predict the labels at new data points. The goal is to achieve small prediction errors. In symbolic regression, the goal is more ambitious, namely, to learn an interpretable…

Discovering governing equations of complex network dynamics is a fundamental challenge in contemporary science with rich data, which can uncover the mysterious patterns and mechanisms of the formation and evolution of complex phenomena in…

Symbolic regression is the machine learning method for learning functions from data. After a brief overview of the symbolic regression landscape, I will describe the two main challenges that traditional algorithms face: they have an unknown…

We present a novel approach to symbolic regression using vision-capable large language models (LLMs) and the ideas behind Google DeepMind's Funsearch. The LLM is given a plot of a univariate function and tasked with proposing an ansatz for…

Scattering amplitudes at loop level can be expressed in terms of Feynman integrals. The latter satisfy partial differential equations in the kinematical variables. We argue that a good choice of basis for (multi-)loop integrals can lead to…

Implicit Regularization (IReg) is a candidate to become an invariant framework in momentum space to perform Feynman diagram calculations to arbitrary loop order. In this work we present a systematic implementation of our method that…