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Neural network approach to reconstructing spectral functions and complex poles of confined particles
by Thibault Lechien, David Dudal
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Submission summary
| Authors (as registered SciPost users): | David Dudal · Thibault Lechien |
| Submission information | |
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| Preprint Link: | scipost_202203_00028v2 (pdf) |
| Code repository: | https://github.com/thibaultLe/SpectralANN |
| Data repository: | https://github.com/thibaultLe/SpectralANN |
| Date accepted: | 2022-09-21 |
| Date submitted: | 2022-09-16 10:04 |
| Submitted by: | Lechien, Thibault |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Computational |
Abstract
Reconstructing spectral functions from propagator data is difficult as solving the analytic continuation problem or applying an inverse integral transformation are ill-conditioned problems. Recent work has proposed using neural networks to solve this problem and has shown promising results, either matching or improving upon the performance of other methods. We generalize this approach by not only reconstructing spectral functions, but also (possible) pairs of complex poles or an infrared (IR) cutoff. We train our network on physically motivated toy functions, examine the reconstruction accuracy and check its robustness to noise. Encouraging results are found on both toy functions and genuine lattice QCD data for the gluon propagator, suggesting that this approach may lead to significant improvements over current state-of-the-art methods.
Author comments upon resubmission
We hope that with these changes, our work will be considered for publication in SciPost Physics.
List of changes
We would like to thank the reviewer for their helpful comments. Please find below our response.
- The parameter ranges from eqs.(8)-(10) were based on estimates from previous work like [*] and our own preliminary experiments which found that larger ranges rarely fit the imposed constraints.
We have added these references and some extra explanation to the paper (Sect. 2.1).
- In the previous version of the manuscript we indeed only considered the case for a fixed number of poles (namely 3). We agree with the Reviewer’s comment. As such, in order to allow the network to not only reconstruct the location of the poles and residues, but also to determine whether poles are present or not, we now included possible residue parameter values of 0 in the training set. When there are less poles than 3, some residue doublets (the a_j and b_j from eq. (7)) will be exactly 0. The goal is that our network only reconstructs the residues for the poles that are present and sets the other residues to zero.
After retraining the network and running all the tests again, we do get promising results: the network is still able to reconstruct the spectral functions, poles and residues with good accuracy, but it is now also able to reject a pole by setting its residue to (approximately) 0. For example, this behavior is visible in the fourth reconstruction of Figure 2 in the revised manuscript.
We have added this explanation and updated all relevant figures in the paper.
- Concerning our usage of the constraints (11), (14) and (15), we believe there was some confusion because we referred to them as the ‘first, second and third constraints’ in the text, while the latter two are actually not the second and third constraints in the numbered equation list of constraints. In order to avoid this confusion in the revised manuscript, we now explicitly refer to the equation numbers instead of their position in the list (see p5, p7).
- For the values of the IR cut-off σ, we have updated the plots to now also include these visually (see e.g. Figures 2 and 3).
References [*]
• D. Binosi, R.-A. Tripolt, Spectral functions of confined particles, Phys. Lett. B 801 (2020) 135171. arXiv:1904.08172, doi:10.1016/j. physletb.2019.135171
• A.F. Falcão, O. Oliveira, P.J. Silva, Analytic structure of the lattice Landau gauge gluon and ghost propagators, Phys. Rev. D 102 (2020) no.11, 114518. arXiv:2008.02614, doi:10.1103/PhysRevD.102.114518
• D. Dudal, O. Oliveira, P.J. Silva, High precision statistical Landau gauge lattice gluon propagator computation vs. the Gribov-Zwanziger approach, Annals Phys. 397 (2018), 351-364. arXiv:1803.02281, doi:10.1016/j.aop.2018.08.019
Published as SciPost Phys. 13, 097 (2022)