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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2312.02067 |
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| _version_ | 1866911964468346880 |
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| author | Calisto, Francesco Moodie, Ryan Zoia, Simone |
| author_facet | Calisto, Francesco Moodie, Ryan Zoia, Simone |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_02067 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Learning Feynman integrals from differential equations with neural networks Calisto, Francesco Moodie, Ryan Zoia, Simone High Energy Physics - Phenomenology High Energy Physics - Theory 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. |
| title | Learning Feynman integrals from differential equations with neural networks |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2312.02067 |