Jiakang Bao
Hilbert series, machine learning, and applications to physics
Bao, Jiakang; He, Yang-Hui; Hirst, Edward; Hofscheier, Johannes; Kasprzyk, Alexander; Majumder, Suvajit
Authors
Yang-Hui He
Edward Hirst
JOHANNES HOFSCHEIER Johannes.Hofscheier@nottingham.ac.uk
Assistant Professor
ALEXANDER KASPRZYK A.M.KASPRZYK@NOTTINGHAM.AC.UK
Associate Professor
Suvajit Majumder
Abstract
We describe how simple machine learning methods successfully predict geometric properties from Hilbert series (HS). Regressors predict embedding weights in projective space to ∼1 mean absolute error, whilst classifiers predict dimension and Gorenstein index to > 90% accuracy with ∼0.5% standard error. Binary random forest classifiers managed to distinguish whether the underlying HS describes a complete intersection with high accuracies exceeding 95%. Neural networks (NNs) exhibited success identifying HS from a Gorenstein ring to the same order of accuracy, whilst generation of "fake" HS proved trivial for NNs to distinguish from those associated to the three-dimensional Fano varieties considered.
Citation
Bao, J., He, Y., Hirst, E., Hofscheier, J., Kasprzyk, A., & Majumder, S. (2022). Hilbert series, machine learning, and applications to physics. Physics Letters B, 827, Article 136966. https://doi.org/10.1016/j.physletb.2022.136966
Journal Article Type | Article |
---|---|
Acceptance Date | Feb 14, 2022 |
Online Publication Date | Feb 18, 2022 |
Publication Date | Apr 10, 2022 |
Deposit Date | Feb 15, 2022 |
Publicly Available Date | Feb 21, 2022 |
Journal | Physics Letters B |
Print ISSN | 0370-2693 |
Electronic ISSN | 1873-2445 |
Publisher | Elsevier |
Peer Reviewed | Peer Reviewed |
Volume | 827 |
Article Number | 136966 |
DOI | https://doi.org/10.1016/j.physletb.2022.136966 |
Keywords | Nuclear and High Energy Physics |
Public URL | https://nottingham-repository.worktribe.com/output/7468356 |
Publisher URL | https://www.sciencedirect.com/science/article/pii/S0370269322001009 |
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Hilbert series, machine learning, and applications to physics
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Publisher Licence URL
https://creativecommons.org/licenses/by/4.0/
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