The Capabilities of Boltzmann Machines to Detect and Reconstruct Ising System’s Configurations from a Given Temperature
The restricted Boltzmann machine (RBM) is a generative neural network that can learn in an unsupervised way. This machine has been proven to help understand complex systems, using its ability to generate samples of the system with the same observed distribution. In this work, an Ising system is simu...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-12-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/25/12/1649 |
| _version_ | 1827574812064612352 |
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| author | Mauricio A. Valle |
| author_facet | Mauricio A. Valle |
| author_sort | Mauricio A. Valle |
| collection | DOAJ |
| description | The restricted Boltzmann machine (RBM) is a generative neural network that can learn in an unsupervised way. This machine has been proven to help understand complex systems, using its ability to generate samples of the system with the same observed distribution. In this work, an Ising system is simulated, creating configurations via Monte Carlo sampling and then using them to train RBMs at different temperatures. Then, 1. the ability of the machine to reconstruct system configurations and 2. its ability to be used as a detector of configurations at specific temperatures are evaluated. The results indicate that the RBM reconstructs configurations following a distribution similar to the original one, but only when the system is in a disordered phase. In an ordered phase, the RBM faces levels of irreproducibility of the configurations in the presence of bimodality, even when the physical observables agree with the theoretical ones. On the other hand, independent of the phase of the system, the information embodied in the neural network weights is sufficient to discriminate whether the configurations come from a given temperature well. The learned representations of the RBM can discriminate system configurations at different temperatures, promising interesting applications in real systems that could help recognize crossover phenomena. |
| first_indexed | 2024-03-08T20:47:24Z |
| format | Article |
| id | doaj.art-06d7dd85a21b4d789e740a411b32d1f4 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-08T20:47:24Z |
| publishDate | 2023-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-06d7dd85a21b4d789e740a411b32d1f42023-12-22T14:07:30ZengMDPI AGEntropy1099-43002023-12-012512164910.3390/e25121649The Capabilities of Boltzmann Machines to Detect and Reconstruct Ising System’s Configurations from a Given TemperatureMauricio A. Valle0Facultad de Economía y Negocios, Universidad Finis Terrae, Santiago 7501015, ChileThe restricted Boltzmann machine (RBM) is a generative neural network that can learn in an unsupervised way. This machine has been proven to help understand complex systems, using its ability to generate samples of the system with the same observed distribution. In this work, an Ising system is simulated, creating configurations via Monte Carlo sampling and then using them to train RBMs at different temperatures. Then, 1. the ability of the machine to reconstruct system configurations and 2. its ability to be used as a detector of configurations at specific temperatures are evaluated. The results indicate that the RBM reconstructs configurations following a distribution similar to the original one, but only when the system is in a disordered phase. In an ordered phase, the RBM faces levels of irreproducibility of the configurations in the presence of bimodality, even when the physical observables agree with the theoretical ones. On the other hand, independent of the phase of the system, the information embodied in the neural network weights is sufficient to discriminate whether the configurations come from a given temperature well. The learned representations of the RBM can discriminate system configurations at different temperatures, promising interesting applications in real systems that could help recognize crossover phenomena.https://www.mdpi.com/1099-4300/25/12/1649restricted Boltzmann machineIsing modellearning representationmultilayer perceptroncrossover |
| spellingShingle | Mauricio A. Valle The Capabilities of Boltzmann Machines to Detect and Reconstruct Ising System’s Configurations from a Given Temperature Entropy restricted Boltzmann machine Ising model learning representation multilayer perceptron crossover |
| title | The Capabilities of Boltzmann Machines to Detect and Reconstruct Ising System’s Configurations from a Given Temperature |
| title_full | The Capabilities of Boltzmann Machines to Detect and Reconstruct Ising System’s Configurations from a Given Temperature |
| title_fullStr | The Capabilities of Boltzmann Machines to Detect and Reconstruct Ising System’s Configurations from a Given Temperature |
| title_full_unstemmed | The Capabilities of Boltzmann Machines to Detect and Reconstruct Ising System’s Configurations from a Given Temperature |
| title_short | The Capabilities of Boltzmann Machines to Detect and Reconstruct Ising System’s Configurations from a Given Temperature |
| title_sort | capabilities of boltzmann machines to detect and reconstruct ising system s configurations from a given temperature |
| topic | restricted Boltzmann machine Ising model learning representation multilayer perceptron crossover |
| url | https://www.mdpi.com/1099-4300/25/12/1649 |
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