Predicting Feynman periods in $ϕ^4$-theory
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arXiv
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| Format: | Preprint |
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2024
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| author | Balduf, Paul-Hermann Shaban, Kimia |
| author_facet | Balduf, Paul-Hermann Shaban, Kimia |
| contents | We present efficient data-driven approaches to predict Feynman periods in $ϕ^4$-theory from properties of the underlying Feynman graphs. We find that the numbers of cuts and cycles determines the period to approximately 2% accuracy. Hepp bound and Martin invariant allow to predict the period with accuracy much better than 1%. In most cases, the period is a multi-linear function of the parameters in question. Besides classical correlation analysis, we also investigate the usefulness of machine-learning algorithms to predict the period. When sufficiently many properties of the graph are used, the period can be predicted with better than 0.05% relative accuracy.
We use one of the constructed prediction models for weighted Monte-Carlo sampling of Feynman graphs, and compute the primitive contribution to the beta function of $ϕ^4$-theory at $L\in \left \lbrace 13, 14, 15, 16 \right \rbrace $ loops. Our results confirm the previously known numerical estimates of the primitive beta function and improve their accuracy. Compared to uniform random sampling of graphs, our new algorithm reaches 35-fold higher accuracy in fixed runtime, or requires 1000-fold less runtime to reach a given accuracy.
The data set of all periods computed for this work, combined with a previous data set, is made publicly available. Besides the physical application, it could serve as a benchmark for graph-based machine learning algorithms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_16217 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Predicting Feynman periods in $ϕ^4$-theory Balduf, Paul-Hermann Shaban, Kimia High Energy Physics - Theory 81T18, 81Q30, 05C30, 05C31 We present efficient data-driven approaches to predict Feynman periods in $ϕ^4$-theory from properties of the underlying Feynman graphs. We find that the numbers of cuts and cycles determines the period to approximately 2% accuracy. Hepp bound and Martin invariant allow to predict the period with accuracy much better than 1%. In most cases, the period is a multi-linear function of the parameters in question. Besides classical correlation analysis, we also investigate the usefulness of machine-learning algorithms to predict the period. When sufficiently many properties of the graph are used, the period can be predicted with better than 0.05% relative accuracy. We use one of the constructed prediction models for weighted Monte-Carlo sampling of Feynman graphs, and compute the primitive contribution to the beta function of $ϕ^4$-theory at $L\in \left \lbrace 13, 14, 15, 16 \right \rbrace $ loops. Our results confirm the previously known numerical estimates of the primitive beta function and improve their accuracy. Compared to uniform random sampling of graphs, our new algorithm reaches 35-fold higher accuracy in fixed runtime, or requires 1000-fold less runtime to reach a given accuracy. The data set of all periods computed for this work, combined with a previous data set, is made publicly available. Besides the physical application, it could serve as a benchmark for graph-based machine learning algorithms. |
| title | Predicting Feynman periods in $ϕ^4$-theory |
| topic | High Energy Physics - Theory 81T18, 81Q30, 05C30, 05C31 |
| url | https://arxiv.org/abs/2403.16217 |