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Learning Feynman integrals from differential equations with neural networks

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arxiv 2312.02067 v2 pith:DJJSWTZ3 submitted 2023-12-04 hep-ph hep-th

classification hep-phhep-th
keywords differentialequationsfeynmanintegralsapplyapproachframeworklearning
verification ladder T0 review T1 audit T2 compute T3 formal
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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 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 bottleneck for the analytical techniques, nor on the availability of a large dataset, and after training yields essentially instantaneous evaluation times. We provide a proof-of-concept implementation within the PyTorch framework, and apply it to a number of one- and two-loop examples, achieving a mean magnitude of relative difference of around 1% at two loops in the physical phase space with network training times on the order of an hour on a laptop GPU.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. FeynmanBench: Benchmarking Multimodal LLMs on Diagrammatic Physics Reasoning

    cs.AI 2026-04 unverdicted novelty 8.0 of 10

    FeynmanBench is the first benchmark for evaluating multimodal LLMs on diagrammatic reasoning with Feynman diagrams, revealing systematic failures in enforcing physical constraints and global topology.

  2. Analytic two-loop amplitudes for $q\bar{q}\to \gamma \gamma$ and $gg \to \gamma \gamma$ mediated by a heavy-quark loop

    hep-ph 2025-01 accept novelty 8.0 of 10

    The two-loop amplitudes for q qbar -> gamma gamma and gg -> gamma gamma with a heavy-quark loop are computed analytically in terms of elliptic iterated integrals, with validated fast series expansions for numerical ev...

  3. First look at the evaluation of two-loop Feynman integrals for radiative return processes

    hep-ph 2026-07 accept novelty 6.0 of 10

    Planar two-loop four-point master integrals for massive radiative-return QED, including elliptic and nested-root sectors, are reduced to polynomial-in-ε differential equations that evaluate stably in the physical region.

  4. All planar three-loop Feynman integrals for the production of two vector bosons at hadron colliders

    hep-ph 2025-12 accept novelty 6.0 of 10

    All nine planar three-loop four-point integral families for two massive external legs are cast into canonical differential equations and evaluated numerically, completing the set needed for leading-colour N3LO diboson...

  5. Explainable AI-assisted Optimization for Feynman Integral Reduction

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    FunSearch discovered a simple priority function for ordering IBP seeding integrals, reducing the number needed for multi-loop Feynman integral reductions by factors up to 3058.

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