A New Look at the Spin Glass Problem from a Deep Learning Perspective
Spin glass is the simplest disordered system that preserves the full range of complex collective behavior of interacting frustrating elements. In the paper, we propose a novel approach for calculating the values of thermodynamic averages of the frustrated spin glass model using custom deep neural ne...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-05-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/24/5/697 |
| _version_ | 1797499997113024512 |
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| author | Petr Andriushchenko Dmitrii Kapitan Vitalii Kapitan |
| author_facet | Petr Andriushchenko Dmitrii Kapitan Vitalii Kapitan |
| author_sort | Petr Andriushchenko |
| collection | DOAJ |
| description | Spin glass is the simplest disordered system that preserves the full range of complex collective behavior of interacting frustrating elements. In the paper, we propose a novel approach for calculating the values of thermodynamic averages of the frustrated spin glass model using custom deep neural networks. The spin glass system was considered as a specific weighted graph whose spatial distribution of the edges values determines the fundamental characteristics of the system. Special neural network architectures that mimic the structure of spin lattices have been proposed, which has increased the speed of learning and the accuracy of the predictions compared to the basic solution of fully connected neural networks. At the same time, the use of trained neural networks can reduce simulation time by orders of magnitude compared to other classical methods. The validity of the results is confirmed by comparison with numerical simulation with the replica-exchange Monte Carlo method. |
| first_indexed | 2024-03-10T03:56:29Z |
| format | Article |
| id | doaj.art-c8d71216f06b4d3fb5f4fc545b5cb38b |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T03:56:29Z |
| publishDate | 2022-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-c8d71216f06b4d3fb5f4fc545b5cb38b2023-11-23T10:55:51ZengMDPI AGEntropy1099-43002022-05-0124569710.3390/e24050697A New Look at the Spin Glass Problem from a Deep Learning PerspectivePetr Andriushchenko0Dmitrii Kapitan1Vitalii Kapitan2National Center for Cognitive Research, ITMO University, bldg. A, Kronverksky Pr. 49, 197101 Saint Petersburg, RussiaNational Center for Cognitive Research, ITMO University, bldg. A, Kronverksky Pr. 49, 197101 Saint Petersburg, RussiaDepartment of Theoretical Physics and Smart Technologies, Far Eastern Federal University, Russky Island, 10 Ajax Bay, 690922 Vladivostok, RussiaSpin glass is the simplest disordered system that preserves the full range of complex collective behavior of interacting frustrating elements. In the paper, we propose a novel approach for calculating the values of thermodynamic averages of the frustrated spin glass model using custom deep neural networks. The spin glass system was considered as a specific weighted graph whose spatial distribution of the edges values determines the fundamental characteristics of the system. Special neural network architectures that mimic the structure of spin lattices have been proposed, which has increased the speed of learning and the accuracy of the predictions compared to the basic solution of fully connected neural networks. At the same time, the use of trained neural networks can reduce simulation time by orders of magnitude compared to other classical methods. The validity of the results is confirmed by comparison with numerical simulation with the replica-exchange Monte Carlo method.https://www.mdpi.com/1099-4300/24/5/697spin glassIsing modelmachine learningdeep neural network |
| spellingShingle | Petr Andriushchenko Dmitrii Kapitan Vitalii Kapitan A New Look at the Spin Glass Problem from a Deep Learning Perspective Entropy spin glass Ising model machine learning deep neural network |
| title | A New Look at the Spin Glass Problem from a Deep Learning Perspective |
| title_full | A New Look at the Spin Glass Problem from a Deep Learning Perspective |
| title_fullStr | A New Look at the Spin Glass Problem from a Deep Learning Perspective |
| title_full_unstemmed | A New Look at the Spin Glass Problem from a Deep Learning Perspective |
| title_short | A New Look at the Spin Glass Problem from a Deep Learning Perspective |
| title_sort | new look at the spin glass problem from a deep learning perspective |
| topic | spin glass Ising model machine learning deep neural network |
| url | https://www.mdpi.com/1099-4300/24/5/697 |
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