SciPost Submission Page
Targeting Multi-Loop Integrals with Neural Networks
by Ramon Winterhalder, Vitaly Magerya, Emilio Villa, Stephen P. Jones, Matthias Kerner, Anja Butter, Gudrun Heinrich, Tilman Plehn
This is not the latest submitted version.
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Gudrun Heinrich · Tilman Plehn · Ramon Winterhalder |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2112.09145v1 (pdf) |
| Date submitted: | 2022-01-03 13:03 |
| Submitted by: | Winterhalder, Ramon |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approaches: | Theoretical, Computational |
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.
Current status:
Reports on this Submission
Report #1 by Anonymous (Referee 1) on 2022-2-15 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2112.09145v1, delivered 2022-02-15, doi: 10.21468/SciPost.Report.4432
Strengths
1 - The authors clearly state the problem they are trying to solve in a easy to understand manner for non-experts.
2 - The authors provide an excellent description of their studies and methodology for solving the problem
Weaknesses
1 - The authors mention speed improvements, but give no hard evidence for this
Report
In this work, the authors develop a machine learning method to improve the performance of contour integration for multi-loop integrals. They devise two steps to improve the overall performance. Firstly, they optimize the deformation parameters through a log-space search algorithm. Then they use machine learning to further improve the sampling of the integral. This work starts to address the difficulties of numerically evaluating multi-loop integrals. By connecting machine learning methods to improve integration, the authors provide new method for efficiently calculating these integrals. This work meets the acceptance criteria for SciPost. However, there are a few issues that need to be resolved before publication as listed in the requested changes section. The most important issue is that the authors mention possible time improvements without evidence, other than training times as a function of batch size.
Requested changes
1 - In the Example diagrams section, the authors describe an example as to where the diagram would show up in calculations. However, the authors do not do so for the lower left diagram of Figure 1. The authors should add this description.
2 - In the first paragraph of Section 3.3, the authors mention that the Jacobian of the complex mapping is computationally more expensive. However, it is unclear to what the computation is more expensive than. Is it the normalizing flow? The original method?
3 - Figure 7 is referenced before Figure 6. The authors should switch the ordering to match the order they are introduced.
4 - The authors make a comment about the timings not being competitive with pySecDec, with the complex-valued determinants being one of the driving factors. And again mention the improvement in speed in the outlook. However, the authors make no comparison of the timings. It would be informative to the reader to have a plot showing the time required to achieve a given precision. This would be helpful in understanding when this algorithm might be better than default pySecDec.