Electronic Research Archive (Jul 2024)

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

  • Jinjun Yong,
  • Xianbing Luo,
  • Shuyu Sun

DOI
https://doi.org/10.3934/era.2024193
Journal volume & issue
Vol. 32, no. 7
pp. 4291 – 4320

Abstract

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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.

Keywords