Deep multi-input and multi-output operator networks method for optimal control of PDEs

Deep operator networks is a popular machine learning approach. Some problems require multiple inputs and outputs. In this work, a multi-input and multi-output operator neural network (MIMOONet) for solving optimal control problems was proposed. To improve the accuracy of the numerical solution, a ph...

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Bibliographic Details
Published inElectronic research archive Vol. 32; no. 7; pp. 4291 - 4320
Main Authors Yong, Jinjun, Luo, Xianbing, Sun, Shuyu
Format Journal Article
LanguageEnglish
Published AIMS Press 01.07.2024
Subjects
multi-input
multi-output
operator neural networks
pde optimal control
physics-informed
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Summary:Deep operator networks is a popular machine learning approach. Some problems require multiple inputs and outputs. In this work, a multi-input and multi-output operator neural network (MIMOONet) for solving optimal control problems was proposed. To improve the accuracy of the numerical solution, a physics-informed MIMOONet was also proposed. To test the performance of the MIMOONet and the physics-informed MIMOONet, three examples, including elliptic (linear and semi-linear) and parabolic problems, were presented. The numerical results show that both methods are effective in solving these types of problems, and the physics-informed MIMOONet achieves higher accuracy due to its incorporation of physical laws.
ISSN:2688-1594
2688-1594
DOI:10.3934/era.2024193