Machine Learning Topological Invariants with Neural Networks
In this Letter we supervisedly train neural networks to distinguish different topological phases in the context of topological band insulators. After training with Hamiltonians of one-dimensional insulators with chiral symmetry, the neural network can predict their topological winding numbers with n...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
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American Physical Society
2018
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| Online Access: | http://hdl.handle.net/1721.1/114406 |
| _version_ | 1811071252503199744 |
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| author | Zhang, Pengfei Shen, Huitao Zhai, Hui |
| author2 | Massachusetts Institute of Technology. Department of Physics |
| author_facet | Massachusetts Institute of Technology. Department of Physics Zhang, Pengfei Shen, Huitao Zhai, Hui |
| author_sort | Zhang, Pengfei |
| collection | MIT |
| description | In this Letter we supervisedly train neural networks to distinguish different topological phases in the context of topological band insulators. After training with Hamiltonians of one-dimensional insulators with chiral symmetry, the neural network can predict their topological winding numbers with nearly 100% accuracy, even for Hamiltonians with larger winding numbers that are not included in the training data. These results show a remarkable success that the neural network can capture the global and nonlinear topological features of quantum phases from local inputs. By opening up the neural network, we confirm that the network does learn the discrete version of the winding number formula. We also make a couple of remarks regarding the role of the symmetry and the opposite effect of regularization techniques when applying machine learning to physical systems. |
| first_indexed | 2024-09-23T08:48:21Z |
| format | Article |
| id | mit-1721.1/114406 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T08:48:21Z |
| publishDate | 2018 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1144062022-09-30T11:23:04Z Machine Learning Topological Invariants with Neural Networks Zhang, Pengfei Shen, Huitao Zhai, Hui Massachusetts Institute of Technology. Department of Physics Shen, Huitao In this Letter we supervisedly train neural networks to distinguish different topological phases in the context of topological band insulators. After training with Hamiltonians of one-dimensional insulators with chiral symmetry, the neural network can predict their topological winding numbers with nearly 100% accuracy, even for Hamiltonians with larger winding numbers that are not included in the training data. These results show a remarkable success that the neural network can capture the global and nonlinear topological features of quantum phases from local inputs. By opening up the neural network, we confirm that the network does learn the discrete version of the winding number formula. We also make a couple of remarks regarding the role of the symmetry and the opposite effect of regularization techniques when applying machine learning to physical systems. 2018-03-27T17:33:08Z 2018-03-27T17:33:08Z 2018-02 2017-12 2018-02-07T18:00:52Z Article http://purl.org/eprint/type/JournalArticle 0031-9007 1079-7114 http://hdl.handle.net/1721.1/114406 Zhang, Pengfei et al. "Machine Learning Topological Invariants with Neural Networks." Physical Review Letters 120, 6 (February 2018): 066401 © 2018 American Physical Society en http://dx.doi.org/10.1103/PhysRevLett.120.066401 Physical Review Letters Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Zhang, Pengfei Shen, Huitao Zhai, Hui Machine Learning Topological Invariants with Neural Networks |
| title | Machine Learning Topological Invariants with Neural Networks |
| title_full | Machine Learning Topological Invariants with Neural Networks |
| title_fullStr | Machine Learning Topological Invariants with Neural Networks |
| title_full_unstemmed | Machine Learning Topological Invariants with Neural Networks |
| title_short | Machine Learning Topological Invariants with Neural Networks |
| title_sort | machine learning topological invariants with neural networks |
| url | http://hdl.handle.net/1721.1/114406 |
| work_keys_str_mv | AT zhangpengfei machinelearningtopologicalinvariantswithneuralnetworks AT shenhuitao machinelearningtopologicalinvariantswithneuralnetworks AT zhaihui machinelearningtopologicalinvariantswithneuralnetworks |