Deep Learning Spinfoam Vertex Amplitudes: The Euclidean Barrett–Crane Model

Spinfoam theories propose a well-defined path-integral formulation for quantum gravity, and it is hoped that they will provide the dynamics of loop quantum gravity. However, it is computationally hard to calculate spinfoam amplitudes. The well-studied Euclidean Barrett–Crane model provides an excell...

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Main Authors: Hanno Sahlmann, Waleed Sherif
Format: Article
Language:English
Published: MDPI AG 2025-07-01
Series:Universe
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Online Access:https://www.mdpi.com/2218-1997/11/7/235
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author Hanno Sahlmann
Waleed Sherif
author_facet Hanno Sahlmann
Waleed Sherif
author_sort Hanno Sahlmann
collection DOAJ
description Spinfoam theories propose a well-defined path-integral formulation for quantum gravity, and it is hoped that they will provide the dynamics of loop quantum gravity. However, it is computationally hard to calculate spinfoam amplitudes. The well-studied Euclidean Barrett–Crane model provides an excellent setting for testing analytical and numerical tools to probe spinfoam models. We explore a data-driven approach to accelerating spinfoam computations by showing that the vertex amplitude is an object that can be learned from data using deep learning. We divide the learning process into a classification and a regression task: Two networks are independently engineered to decide whether the amplitude is zero or not and to predict the precise numerical value, respectively. The trained networks are tested with several accuracy measures. The classifier in particular demonstrates robust generalisation far outside the training domain, while the regressor demonstrates high predictive accuracy in the domain it is trained on. We discuss limitations, possible improvements, and implications for future work.
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spelling doaj-art-c13fdfc569be4da18f26b2c5d7a1ec382025-08-20T02:47:10ZengMDPI AGUniverse2218-19972025-07-0111723510.3390/universe11070235Deep Learning Spinfoam Vertex Amplitudes: The Euclidean Barrett–Crane ModelHanno Sahlmann0Waleed Sherif1Institute for Quantum Gravity, Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Staudtstraße 7, 91058 Erlangen, GermanyInstitute for Quantum Gravity, Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Staudtstraße 7, 91058 Erlangen, GermanySpinfoam theories propose a well-defined path-integral formulation for quantum gravity, and it is hoped that they will provide the dynamics of loop quantum gravity. However, it is computationally hard to calculate spinfoam amplitudes. The well-studied Euclidean Barrett–Crane model provides an excellent setting for testing analytical and numerical tools to probe spinfoam models. We explore a data-driven approach to accelerating spinfoam computations by showing that the vertex amplitude is an object that can be learned from data using deep learning. We divide the learning process into a classification and a regression task: Two networks are independently engineered to decide whether the amplitude is zero or not and to predict the precise numerical value, respectively. The trained networks are tested with several accuracy measures. The classifier in particular demonstrates robust generalisation far outside the training domain, while the regressor demonstrates high predictive accuracy in the domain it is trained on. We discuss limitations, possible improvements, and implications for future work.https://www.mdpi.com/2218-1997/11/7/235loop quantum gravityspinfoamsdeep learningnumerical calculations
spellingShingle Hanno Sahlmann
Waleed Sherif
Deep Learning Spinfoam Vertex Amplitudes: The Euclidean Barrett–Crane Model
Universe
loop quantum gravity
spinfoams
deep learning
numerical calculations
title Deep Learning Spinfoam Vertex Amplitudes: The Euclidean Barrett–Crane Model
title_full Deep Learning Spinfoam Vertex Amplitudes: The Euclidean Barrett–Crane Model
title_fullStr Deep Learning Spinfoam Vertex Amplitudes: The Euclidean Barrett–Crane Model
title_full_unstemmed Deep Learning Spinfoam Vertex Amplitudes: The Euclidean Barrett–Crane Model
title_short Deep Learning Spinfoam Vertex Amplitudes: The Euclidean Barrett–Crane Model
title_sort deep learning spinfoam vertex amplitudes the euclidean barrett crane model
topic loop quantum gravity
spinfoams
deep learning
numerical calculations
url https://www.mdpi.com/2218-1997/11/7/235
work_keys_str_mv AT hannosahlmann deeplearningspinfoamvertexamplitudestheeuclideanbarrettcranemodel
AT waleedsherif deeplearningspinfoamvertexamplitudestheeuclideanbarrettcranemodel