Targeting Multi-Loop Integrals with Neural Networks

Abstract

Numerical evaluations of Feynman integrals often proceed via a deformation of the integration contour into the complex plane. While valid contours are easy to construct, the numerical precision for a multi-loop integral can depend critically on the chosen contour. We present methods to optimize this contour using a combination of optimized, global complex shifts and a normalizing flow. They can lead to a significant gain in precision.

20 pages, 9 figures, v3: added two references

References in corpus (20)

• NICE: Non-linear Independent Components Estimation
• Guided Image Generation with Conditional Invertible Neural Networks
• Sector Decomposition
• Two-loop planar master integrals for Higgs$\to 3$ partons with full heavy-quark mass dependence
• Collider Physics at the Precision Frontier
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Cited by in corpus (29)

• Machine Learning and LHC Event Generation
• Event Generators for High-Energy Physics Experiments
• Evaluation of Feynman integrals with arbitrary complex masses via series expansions
• MadNIS -- Neural Multi-Channel Importance Sampling
• Les Houches 2021: Physics at TeV Colliders: Report on the Standard Model Precision Wishlist
• Two Invertible Networks for the Matrix Element Method
• Quantum algorithm for Feynman loop integrals
• The MadNIS Reloaded
• CaloFlow for CaloChallenge Dataset 1
• Ephemeral Learning -- Augmenting Triggers with Online-Trained Normalizing Flows
• Comparing Machine Learning and Interpolation Methods for Loop-Level Calculations
• Precision-Machine Learning for the Matrix Element Method
• ELSA -- Enhanced latent spaces for improved collider simulations
• Calorimeter shower superresolution
• Differentiable MadNIS-Lite
• Accurate Surrogate Amplitudes with Calibrated Uncertainties
• Anomaly detection with flow-based fast calorimeter simulators
• PIPPIN: Generating variable length full events from partons
• Learning Feynman integrals from differential equations with neural networks
• Sampling NNLO QCD phase space with normalizing flows
• Machine Learning Post-Minkowskian Integrals
• Learning the Simplicity of Scattering Amplitudes
• TopicFlow: Disentangling quark and gluon jets with normalizing flows
• Unifying Simulation and Inference with Normalizing Flows
• Amplitude Uncertainties Everywhere All at Once
• Extrapolating Jet Radiation with Autoregressive Transformers
• BitHEP -- The Limits of Low-Precision ML in HEP
• Event Generation and Density Estimation with Surjective Normalizing Flows
• Amplitude Surrogates for Multi-Jet Processes