Applications of neural networks to the simulation of dynamics of open quantum systems
Despite neural networks’ success, their applications to open-system dynamics are few. In this work, non-linear autoregressive neural networks are adopted to generalize time series of expectation values of observables of interest in open quantum systems. Using Dirac-Frenkel time-dependent variation w...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2020
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| Online Access: | https://hdl.handle.net/10356/136768 |
| _version_ | 1826125633200062464 |
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| author | Bandyopadhyay, Sayantan Huang, Zhongkai Sun, Kewei Zhao, Yang |
| author2 | School of Materials Science & Engineering |
| author_facet | School of Materials Science & Engineering Bandyopadhyay, Sayantan Huang, Zhongkai Sun, Kewei Zhao, Yang |
| author_sort | Bandyopadhyay, Sayantan |
| collection | NTU |
| description | Despite neural networks’ success, their applications to open-system dynamics are few. In this work, non-linear autoregressive neural networks are adopted to generalize time series of expectation values of observables of interest in open quantum systems. Using Dirac-Frenkel time-dependent variation with the multiple Davydov D2 Ansatz, we obtain first stages of dynamical states of both the spin-boson model and the dissipative Landau-Zener model. With calculated data, careful training of the non-linear neural networks is performed. It is shown that the training quality of the networks is sufficient to ensure a least mean square error of 1×10-11. Subsequently, the network is cross validated by testing with additional data. Successes of the network training demonstrate that initial data of simulated open-system dynamics contain sufficient knowledge regarding its future propagation. We use the first-stage information and the trained network to predict future values of target observables in the series, and succeed with considerable accuracy. |
| first_indexed | 2024-10-01T06:39:32Z |
| format | Journal Article |
| id | ntu-10356/136768 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T06:39:32Z |
| publishDate | 2020 |
| record_format | dspace |
| spelling | ntu-10356/1367682023-07-14T15:48:56Z Applications of neural networks to the simulation of dynamics of open quantum systems Bandyopadhyay, Sayantan Huang, Zhongkai Sun, Kewei Zhao, Yang School of Materials Science & Engineering Engineering::Materials Neural Networks Open Quantum Systems Despite neural networks’ success, their applications to open-system dynamics are few. In this work, non-linear autoregressive neural networks are adopted to generalize time series of expectation values of observables of interest in open quantum systems. Using Dirac-Frenkel time-dependent variation with the multiple Davydov D2 Ansatz, we obtain first stages of dynamical states of both the spin-boson model and the dissipative Landau-Zener model. With calculated data, careful training of the non-linear neural networks is performed. It is shown that the training quality of the networks is sufficient to ensure a least mean square error of 1×10-11. Subsequently, the network is cross validated by testing with additional data. Successes of the network training demonstrate that initial data of simulated open-system dynamics contain sufficient knowledge regarding its future propagation. We use the first-stage information and the trained network to predict future values of target observables in the series, and succeed with considerable accuracy. NRF (Natl Research Foundation, S’pore) MOE (Min. of Education, S’pore) Accepted version 2020-01-23T05:45:54Z 2020-01-23T05:45:54Z 2018 Journal Article Bandyopadhyay, S., Huang, Z., Sun, K., & Zhao, Y. (2018). Applications of neural networks to the simulation of dynamics of open quantum systems. Chemical Physics, 515, 272-278. doi:10.1016/j.chemphys.2018.05.019 0301-0104 https://hdl.handle.net/10356/136768 10.1016/j.chemphys.2018.05.019 2-s2.0-85048586120 515 272 278 en Chemical Physics © 2018 Elsevier B.V. All rights reserved. This paper was published in Chemical Physics and is made available with permission of Elsevier B.V. application/pdf |
| spellingShingle | Engineering::Materials Neural Networks Open Quantum Systems Bandyopadhyay, Sayantan Huang, Zhongkai Sun, Kewei Zhao, Yang Applications of neural networks to the simulation of dynamics of open quantum systems |
| title | Applications of neural networks to the simulation of dynamics of open quantum systems |
| title_full | Applications of neural networks to the simulation of dynamics of open quantum systems |
| title_fullStr | Applications of neural networks to the simulation of dynamics of open quantum systems |
| title_full_unstemmed | Applications of neural networks to the simulation of dynamics of open quantum systems |
| title_short | Applications of neural networks to the simulation of dynamics of open quantum systems |
| title_sort | applications of neural networks to the simulation of dynamics of open quantum systems |
| topic | Engineering::Materials Neural Networks Open Quantum Systems |
| url | https://hdl.handle.net/10356/136768 |
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