PA_CasualLSTM: A new time series prediction network with the physical constraint and adjusted Fourier neural operator for the time-dependent partial differential equation
In this work, a new time series prediction network is proposed in the framework of CasualLSTM with physical constraints and an adjusted Fourier neural operator (FNO) for the solution of the time-dependent partial differential equation. The framework of CasualLSTM is employed to learn the time evolut...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2022-09-01
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| Series: | Frontiers in Physics |
| Subjects: | |
| Online Access: | https://www.frontiersin.org/articles/10.3389/fphy.2022.1004417/full |
| _version_ | 1798001296991584256 |
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| author | Chaohao Xiao Xiaoqian Zhu Xiaoqun Cao Fukang Yin Jun Nie Fujia Hu |
| author_facet | Chaohao Xiao Xiaoqian Zhu Xiaoqun Cao Fukang Yin Jun Nie Fujia Hu |
| author_sort | Chaohao Xiao |
| collection | DOAJ |
| description | In this work, a new time series prediction network is proposed in the framework of CasualLSTM with physical constraints and an adjusted Fourier neural operator (FNO) for the solution of the time-dependent partial differential equation. The framework of CasualLSTM is employed to learn the time evolution of spatial features which strengthens the extrapolation capability. With the help of adjusted Fourier layers (AFLs), residual connection, and the adaptive time-marching strategy, the network can quickly converge and extrapolate without labeled data by encoding PDE constraints into loss functions. Two examples, namely, Burger’s equation and two-dimensional Navier–Stokes (N-S) equation are used to evaluate the proposed method. Numerical results show that the proposed method has a good performance in solution accuracy and extrapolability. |
| first_indexed | 2024-04-11T11:35:08Z |
| format | Article |
| id | doaj.art-cf841c0e27bd4739867b859750cd9ebb |
| institution | Directory Open Access Journal |
| issn | 2296-424X |
| language | English |
| last_indexed | 2024-04-11T11:35:08Z |
| publishDate | 2022-09-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Physics |
| spelling | doaj.art-cf841c0e27bd4739867b859750cd9ebb2022-12-22T04:26:01ZengFrontiers Media S.A.Frontiers in Physics2296-424X2022-09-011010.3389/fphy.2022.10044171004417PA_CasualLSTM: A new time series prediction network with the physical constraint and adjusted Fourier neural operator for the time-dependent partial differential equationChaohao Xiao0Xiaoqian Zhu1Xiaoqun Cao2Fukang Yin3Jun Nie4Fujia Hu5College of Meteorology and Oceanography, National University of Defense Technology, Changsha, ChinaCollege of Meteorology and Oceanography, National University of Defense Technology, Changsha, ChinaCollege of Meteorology and Oceanography, National University of Defense Technology, Changsha, ChinaCollege of Meteorology and Oceanography, National University of Defense Technology, Changsha, China93110 Troops, PLA, Beijing, China95809 Troops, PLA, Cangzhou, ChinaIn this work, a new time series prediction network is proposed in the framework of CasualLSTM with physical constraints and an adjusted Fourier neural operator (FNO) for the solution of the time-dependent partial differential equation. The framework of CasualLSTM is employed to learn the time evolution of spatial features which strengthens the extrapolation capability. With the help of adjusted Fourier layers (AFLs), residual connection, and the adaptive time-marching strategy, the network can quickly converge and extrapolate without labeled data by encoding PDE constraints into loss functions. Two examples, namely, Burger’s equation and two-dimensional Navier–Stokes (N-S) equation are used to evaluate the proposed method. Numerical results show that the proposed method has a good performance in solution accuracy and extrapolability.https://www.frontiersin.org/articles/10.3389/fphy.2022.1004417/fullCasualLSTMpartial differential equationdeep learningadjusted Fourier layersresidual connection |
| spellingShingle | Chaohao Xiao Xiaoqian Zhu Xiaoqun Cao Fukang Yin Jun Nie Fujia Hu PA_CasualLSTM: A new time series prediction network with the physical constraint and adjusted Fourier neural operator for the time-dependent partial differential equation Frontiers in Physics CasualLSTM partial differential equation deep learning adjusted Fourier layers residual connection |
| title | PA_CasualLSTM: A new time series prediction network with the physical constraint and adjusted Fourier neural operator for the time-dependent partial differential equation |
| title_full | PA_CasualLSTM: A new time series prediction network with the physical constraint and adjusted Fourier neural operator for the time-dependent partial differential equation |
| title_fullStr | PA_CasualLSTM: A new time series prediction network with the physical constraint and adjusted Fourier neural operator for the time-dependent partial differential equation |
| title_full_unstemmed | PA_CasualLSTM: A new time series prediction network with the physical constraint and adjusted Fourier neural operator for the time-dependent partial differential equation |
| title_short | PA_CasualLSTM: A new time series prediction network with the physical constraint and adjusted Fourier neural operator for the time-dependent partial differential equation |
| title_sort | pa casuallstm a new time series prediction network with the physical constraint and adjusted fourier neural operator for the time dependent partial differential equation |
| topic | CasualLSTM partial differential equation deep learning adjusted Fourier layers residual connection |
| url | https://www.frontiersin.org/articles/10.3389/fphy.2022.1004417/full |
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