Abstract
We study a neural network framework for the numerical evaluation of Feynman loop integrals that are fundamental building blocks for perturbative computations of physical observables in gauge and gravity theories. We show that such a machine learning approach improves the convergence of the Monte Carlo algorithm for high-precision evaluation of multi-dimensional integrals compared to traditional algorithms. In particular, we use a neural network to improve the importance sampling. For a set of representative integrals appearing in the computation of the conservative dynamics for a compact binary system in General Relativity, we perform a quantitative comparison between the Monte Carlo integrators VEGAS and i-flow, an integrator based on neural network sampling.
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Acknowledgments
The authors are grateful to Stephen Jones, Go Mishima, Andres Pöldaro, Vladyslav Shtabo- venko for helpful correspondence on pySecDec, and to Joshua Isaacson for the support with iflow. We are indebted to Luisa Lucie-Smith for the very effective comments on the draft. We thank Christoph Dlapa and Rafael Porto for useful discussions and collaborations on related topics. This work was supported by the Deutsche Forschungsgemeinschaft under Germany’s Excellence Strategy EXC 2121 ‘Quantum Universe’ (No. 390833306) and EXC 2094 ‘ORIGINS’ (No. 390783311). The work of RJ is supported by the grants IFT Centro de Excelencia Severo Ochoa SEV-2016-0597, CEX2020-001007-S and by PID2019-110058GB- C22 funded by MCIN/AEI/10.13039/501100011033 and by ERDF. The work of RJ is supported by Grants-in-Aid for JSPS Overseas Research Fellow (No. 201960698). GK received support from the ERC-CoG Precision Gravity: from the LHC to LISA provided by the European Research Council (ERC) under the European Union’s H2020 research and innovation programme (grant No. 817791).
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Jinno, R., Kälin, G., Liu, Z. et al. Machine learning Post-Minkowskian integrals. J. High Energ. Phys. 2023, 181 (2023). https://doi.org/10.1007/JHEP07(2023)181
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DOI: https://doi.org/10.1007/JHEP07(2023)181