Research article Special Issues

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

  • Received: 28 May 2024 Revised: 26 June 2024 Accepted: 01 July 2024 Published: 08 July 2024
  • 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.

    Citation: Jinjun Yong, Xianbing Luo, Shuyu Sun. Deep multi-input and multi-output operator networks method for optimal control of PDEs[J]. Electronic Research Archive, 2024, 32(7): 4291-4320. doi: 10.3934/era.2024193

    Related Papers:

  • 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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