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

Jinjun Yong; Xianbing Luo; Shuyu Sun

doi:10.3934/era.2024193

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

Jinjun Yong, Xianbing Luo^*, Shuyu Sun

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	4291-4320
Number of pages	30
Journal	Electronic Research Archive
Volume	32
Issue number	7
DOIs	https://doi.org/10.3934/era.2024193
State	Published - 2024

Bibliographical note

Publisher Copyright:
© (2024) the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)

Keywords

multi-input
multi-output
operator neural networks
PDE optimal control
physics-informed

ASJC Scopus subject areas

General Mathematics

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10.3934/era.2024193

Cite this

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abstract = "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.",

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AU - Sun, Shuyu

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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