@article{Yong2024, 
author = {Jinjun Yong and Xianbing Luo and Shuyu Sun},
title = {Deep multi-input and multi-output operator networks method for optimal control of PDEs},
year = {2024},
journal = {Electronic Research Archive},
volume = {32},
number = {7},
pages = {4291-4320},
keywords = {operator neural networks, multi-input, multi-output, physics-informed, PDE optimal control},
url = {https://www.sciopen.com/article/10.3934/era.2024193},
doi = {10.3934/era.2024193},
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.}
}