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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MDPI AG
2025-07-01
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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. |
| format | Article |
| id | doaj-art-c13fdfc569be4da18f26b2c5d7a1ec38 |
| institution | DOAJ |
| issn | 2218-1997 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | MDPI AG |
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| series | Universe |
| 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 |