×

Machine learning Lie structures & applications to physics. (English) Zbl 07408522

Summary: Classical and exceptional Lie algebras and their representations are among the most important tools in the analysis of symmetry in physical systems. In this letter we show how the computation of tensor products and branching rules of irreducible representations is machine-learnable, and can achieve relative speed-ups of orders of magnitude in comparison to the non-ML algorithms.

MSC:

81-XX Quantum theory
83-XX Relativity and gravitational theory

References:

[1] Slansky, R., Group theory for unified model building, Phys. Rep., 79, 1-128 (1981)
[2] Feger, R.; Kephart, T. W.; Saskowski, R. J., LieART 2.0 - a mathematica application for Lie algebras and representation theory, Comput. Phys. Commun., 257, Article 107490 pp. (2020) · Zbl 1515.17005
[3] He, Y. H., Deep-learning the landscape, Science, 365, 6452 (2019)
[4] He, Y. H., Machine-learning the String Landscape, Phys. Lett. B, 774, 564-568 (2017)
[5] He, Y. H., The Calabi-Yau landscape: from geometry, to physics, to machine-learning, Springer, in press · Zbl 1492.14001
[6] Krefl, D.; Seong, R. K., Machine learning of Calabi-Yau volumes, Phys. Rev. D, 96, 6, Article 066014 pp. (2017)
[7] Ruehle, F., Evolving neural networks with genetic algorithms to study the String Landscape, J. High Energy Phys., 1708, Article 038 pp. (2017) · Zbl 1381.83128
[8] Carifio, J.; Halverson, J.; Krioukov, D.; Nelson, B. D., Machine learning in the String Landscape, J. High Energy Phys., 1709, Article 157 pp. (2017) · Zbl 1382.81155
[9] Brodie, C. R.; Constantin, A.; Deen, R.; Lukas, A., Machine learning line bundle cohomology, Fortschr. Phys., 68, 1, Article 1900087 pp. (2020) · Zbl 1535.32024
[10] Larfors, M.; Schneider, R., Explore and exploit with heterotic line bundle models, Fortschr. Phys., 68, 5, Article 2000034 pp. (2020) · Zbl 1537.81008
[11] He, Y. H.; Lee, S. J., Distinguishing elliptic fibrations with AI, Phys. Lett. B, 798, Article 134889 pp. (2019)
[12] Bull, K.; He, Y. H.; Jejjala, V.; Mishra, C., Machine learning CICY threefolds, Phys. Lett. B, 785, 65 (2018); Bull, K.; He, Y. H.; Jejjala, V.; Mishra, C., Getting CICY high, Phys. Lett. B, 795, 700 (2019) · Zbl 1420.14002
[13] Ashmore, A.; He, Y. H.; Ovrut, B. A., Machine learning Calabi-Yau metrics, Fortschr. Phys., 68, 9, Article 2000068 pp. (2020) · Zbl 1537.53003
[14] He, Y. H.; Kim, M., Learning algebraic structures: preliminary investigations
[15] Alessandretti, L.; Baronchelli, A.; He, Y. H., Machine learning meets number theory: the data science of Birch-Swinnerton-Dyer
[16] He, Y. H.; Hirst, E.; Peterken, T., Machine-learning dessins d’enfants: explorations via modular and Seiberg-Witten curves, J. Phys. A, A54, Article 7 pp. (2021) · Zbl 1519.14058
[17] He, Y. H.; Lee, K. H.; Oliver, T., Machine-learning the Sato-Tate conjecture · Zbl 1483.11133
[18] Bao, J.; Franco, S.; He, Y. H.; Hirst, E.; Musiker, G.; Xiao, Y., Quiver mutations, Seiberg duality and machine learning, Phys. Rev. D
[19] Gal, Y.; Jejjala, V.; Mayorga Pena, D. K.; Mishra, C., Baryons from mesons: a machine learning perspective
[20] Jejjala, V.; Kar, A.; Parrikar, O., Deep learning the hyperbolic volume of a knot, Phys. Lett. B, 799, Article 135033 pp. (2019); Gukov, S.; Halverson, J.; Ruehle, F.; Sułkowski, P., Learning to unknot · Zbl 1430.57001
[21] Deen, R.; He, Y. H.; Lee, S. J.; Lukas, A., ML string standard models
[22] Halverson, J.; Nelson, B.; Ruehle, F., Branes with brains: exploring string vacua with deep RL, J. High Energy Phys., 06, Article 003 pp. (2019) · Zbl 1416.83125
[23] Halverson, J.; Long, C., Statistical predictions in string theory and deep generative models, Fortschr. Phys., 68, 5, Article 2000005 pp. (2020) · Zbl 07763959
[24] He, Y. H.; Yau, S. T., Graph Laplacians, Riemannian manifolds and their machine-learning · Zbl 07623635
[25] Akutagawa, T.; Hashimoto, K.; Sumimoto, T., Phys. Rev. D, 102, 2, Article 026020 pp. (2020)
[26] Koch, E.d.; de Mello Koch, R.; Cheng, L., Is deep learning a renormalization group flow?
[27] Halverson, J.; Maiti, A.; Stoner, K., Neural networks and quantum field theory
[28] Krippendorf, S.; Syvaeri, M., Detecting symmetries with neural networks
[29] Chen, H. Y.; He, Y. H.; Lal, S.; Zaz, M. Z., Machine learning etudes in conformal field theories
[30] Chollet, F., Keras (2015), Github repository
[31] Matthews, B. M., Comparison of the predicted and observed secondary structure of T4 phage lysozyme, Biochim. Biophys. Acta, Protein Struct., 405, 2, 442-451 (1975)
[32] Mathematica version 12.1, Champaign, Il, 2020
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.