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  1. Dec 4, 2023We perform an exploratory study of a new approach for evaluating Feynman integrals numerically. We apply the recently-proposed framework of physics-informed deep learning to train neural networks to approximate the solution to the differential equations satisfied by the Feynman integrals. This approach relies neither on a canonical form of the differential equations, which is often a ...
  2. This approach relies neither on a canonical form of the differential equations, ... differential equations (DEs) [1-6], in which Feynman integrals are viewed as solutions to ... using machine learning to solve the DEs numerically. We use deep NNs as universal function approximators [60], and train them ...
  3. researchgate.net

    Jul 12, 2024A bstract We perform an exploratory study of a new approach for evaluating Feynman integrals numerically. We apply the recently-proposed framework of physics-informed deep learning to train neural ...
  4. ar5iv.labs.arxiv.org

    The interest for Feynman integrals is therefore growing, and so is the effort in the search for techniques for evaluating them. One of the most powerful approaches is the method of differential equations Barucchi:1973zm ; Kotikov:1990kg ; Kotikov:1991hm ; Gehrmann:1999as ; Bern:1993kr ; Henn:2013pwa , in which Feynman integrals are viewed as solutions to certain DEs.
  5. indico.cern.ch

    Learning Feynman integrals from differential equations with neural networks Milan Christmas Meeting, ... Method of differential equations 4 ... 4 = (k−p 4)2 4} Integral families and master integrals 5 Scalar Feynman integrals with the same propagator structure = integral family I a
  6. semanticscholar.org

    Dec 4, 2023An exploratory study of a new approach for evaluating Feynman integrals numerically, which relies neither on a canonical form of the differential equations, nor on the availability of a large dataset, and after training yields essentially instantaneous evaluation times. Abstract We perform an exploratory study of a new approach for evaluating Feynman integrals numerically. We apply the ...
  7. This repository provides some basic examples of using deep neural networks and feed-forward and LSTM-like neural networks to solve ordinary differential equations (ODEs), partial differential equations (PDEs), and integral equations. Neural networks, in general, can approximate the solution of a differential equation based on the Deep Galerkin ...
  8. Over the last year significant progress was made in the understanding of the computation of Feynman integrals using differential equations. These lectures give a review of these developments, while not assuming any prior knowledge of the subject. After an introduction to differential equations for Feynman integrals, we point out how they can be simplified using algorithms available in the ...
  9. onlinelibrary.wiley.com

    Neural networks are increasingly used to construct numerical solution methods for partial differential equations. In this expository review, we introduce and contrast three important recent approaches attractive in their simplicity and their suitability for high-dimensional problems: physics-informed neural networks, methods based on the Feynman-Kac formula and methods based on the solution ...
  10. sciencedirect.com

    Partial differential equations (PDEs) are widely used in the modeling of objective laws in physics, finance and many other disciplines. ... is often replaced by its equivalent form (obtained by integration by parts): W (u ... Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear ...

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