arrow
Volume 14, Issue 3
Real-Time Computing for a Parameterized Feedback Control Problem of Boussinesq Equations by POD and Deep Learning

Guang-Ri Piao & Hyung-Chun Lee

East Asian J. Appl. Math., 14 (2024), pp. 507-529.

Published online: 2024-05

Export citation
  • Abstract

An efficient real-time computational method for a feedback control problem of the Boussinesq equations is studied. We consider a simple and effective feedback control law based on the relationship between the control and adjoint variables in the optimality system. We investigate a closure type modeling in reduced order model (ROM) of this problem for real-time computing. In order to improve the existing well-known POD-ROM method, the deep learning technique, which is currently being actively researched, is studied and applied. Computational results presented show that the suggested methods work well.

  • AMS Subject Headings

65M10, 78A480

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{EAJAM-14-507, author = {Piao , Guang-Ri and Lee , Hyung-Chun}, title = {Real-Time Computing for a Parameterized Feedback Control Problem of Boussinesq Equations by POD and Deep Learning}, journal = {East Asian Journal on Applied Mathematics}, year = {2024}, volume = {14}, number = {3}, pages = {507--529}, abstract = {

An efficient real-time computational method for a feedback control problem of the Boussinesq equations is studied. We consider a simple and effective feedback control law based on the relationship between the control and adjoint variables in the optimality system. We investigate a closure type modeling in reduced order model (ROM) of this problem for real-time computing. In order to improve the existing well-known POD-ROM method, the deep learning technique, which is currently being actively researched, is studied and applied. Computational results presented show that the suggested methods work well.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.2023-094.250623}, url = {http://global-sci.org/intro/article_detail/eajam/23159.html} }
TY - JOUR T1 - Real-Time Computing for a Parameterized Feedback Control Problem of Boussinesq Equations by POD and Deep Learning AU - Piao , Guang-Ri AU - Lee , Hyung-Chun JO - East Asian Journal on Applied Mathematics VL - 3 SP - 507 EP - 529 PY - 2024 DA - 2024/05 SN - 14 DO - http://doi.org/10.4208/eajam.2023-094.250623 UR - https://global-sci.org/intro/article_detail/eajam/23159.html KW - Optimal control, feedback control, Boussinesq, finite element, POD, LSTM. AB -

An efficient real-time computational method for a feedback control problem of the Boussinesq equations is studied. We consider a simple and effective feedback control law based on the relationship between the control and adjoint variables in the optimality system. We investigate a closure type modeling in reduced order model (ROM) of this problem for real-time computing. In order to improve the existing well-known POD-ROM method, the deep learning technique, which is currently being actively researched, is studied and applied. Computational results presented show that the suggested methods work well.

Piao , Guang-Ri and Lee , Hyung-Chun. (2024). Real-Time Computing for a Parameterized Feedback Control Problem of Boussinesq Equations by POD and Deep Learning. East Asian Journal on Applied Mathematics. 14 (3). 507-529. doi:10.4208/eajam.2023-094.250623
Copy to clipboard
The citation has been copied to your clipboard