Abstract
Theory-guided neural network recently has been used to solve partial differential equations. This method has received widespread attention due to its low data requirements and adherence to physical laws during the training process. However, the selection of the punishment coefficient for including physical laws as a penalty term in the loss function undoubtedly affects the performance of the model. In this paper, we propose a comprehensive theory-guided framework using a bilevel programming model that can adaptively adjust the hyperparameters of the loss function to further enhance the performance of the model. An enhanced water flow optimizer (EWFO) algorithm is applied to optimize upper-level variables in the framework. In this algorithm, an opposition-based learning technic is used in the initialization phase to boost the initial group quality; a nonlinear convergence factor is added to the laminar flow operator to upgrade the diversity of the group and expand the search range. The experiments show that competitive performance of the method in solving stochastic partial differential equations.
This work was supported in part by the National Key R &D Program of China under Grant 2019YFA0708700; in part by the National Natural Science Foundation of China under Grant 62173345; and in part by the Fundamental Research Funds for the Central Universities under Grant 22CX03002A; and in part by the China-CEEC Higher Education Institutions Consortium Program under Grant 2022151; and in part by the Introduction Plan for High Talent Foreign Experts under Grant G2023152012L; and in part by the “The Belt and Road” Innovative Talents Exchange Foreign Experts Project under Grant DL2023152001L; and in part by SDAIA-KFUPM Joint Research Center for Artificial Intelligence under grant no. JRC-AI-RFP-04.
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References
Pao-Liu, C.: Stochastic Partial Differential Equations. CRC Press, Boca Raton (2014)
Ghanem, R.G., Spanos, P.D.: Stochastic finite elements: a spectral approach. Courier Corporation (2003)
Gong, X., Yu, L., Wang, J., Zhang, K., Bai, X., Pal, N.R.: Unsupervised feature selection via adaptive autoencoder with redundancy control. Neural Netw. 150, 87–101 (2022)
Jones, D.R., Schonlau, M., Welch, W.J.: Efficient global optimization of expensive black-box functions. J. Global Optim. 13(4), 455 (1998)
Kingma, D.P., Ba, J.: Adam: a method for stochastic optimization. arXiv preprint arXiv:1412.6980 (2014)
Li, J., Wang, X., Xue, G., Zhang, H., Wang, J.: Sparse broad learning system via a novel competitive swarm optimizer. In: 2022 IEEE 6th Advanced Information Technology, Electronic and Automation Control Conference (IAEAC), pp. 1697–1701. IEEE (2022)
Liao, Q., Lei, G., Zhang, D., Patil, S.: Analytical solution for upscaling hydraulic conductivity in anisotropic heterogeneous formations. Adv. Water Resour. 128, 97–116 (2019)
Luo, K.: Water flow optimizer: a nature-inspired evolutionary algorithm for global optimization. IEEE Trans. Cybern. 52(8), 7753–7764 (2021)
Pardoux, É.: Stochastic Partial Differential Equations: An Introduction. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-89003-2
Raissi, M., Perdikaris, P., Karniadakis, G.E.: Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J. Comput. Phys. 378, 686–707 (2019)
Wang, J., Pang, X., Yin, F., Yao, J.: A deep neural network method for solving partial differential equations with complex boundary in groundwater seepage. J. Petrol. Sci. Eng. 209, 109880 (2022)
Wang, N., Chang, H., Zhang, D.: Efficient uncertainty quantification and data assimilation via theory-guided convolutional neural network. SPE J. 26(06), 4128–4156 (2021)
Wang, N., Liao, Q., Chang, H., Zhang, D.: Deep-learning-based upscaling method for geologic models via theory-guided convolutional neural network. arXiv preprint arXiv:2201.00698 (2021)
Wen, X.-H., Gómez-Hernández, J.J.: Upscaling hydraulic conductivities in heterogeneous media: an overview. J. Hydrol. 183(1–2), 9–27 (1996)
Zhang, B., Gong, X., Wang, J., Tang, F., Zhang, K., Wei, W.: Nonstationary fuzzy neural network based on FCMnet clustering and a modified CG method with Armijo-type rule. Inf. Sci. 608, 313–338 (2022)
Zhou, Y., Wang, R., Luo, Q.: Elite opposition-based flower pollination algorithm. Neurocomputing 188, 294–310 (2016)
Acknowledgements
This work was supported in part by the National Key R &D Program of China under Grant 2019YFA0708700; in part by the National Natural Science Foundation of China under Grant 62173345; and in part by the Fundamental Research Funds for the Central Universities under Grant 22CX03002A; and in part by the China-CEEC Higher Education Institutions Consortium Program under Grant 2022151; and in part by the Introduction Plan for High Talent Foreign Experts under Grant G2023152012L; and in part by the “The Belt and Road” Innovative Talents Exchange Foreign Experts Project under Grant DL2023152001L; and in part by SDAIA-KFUPM Joint Research Center for Artificial Intelligence under grant no. JRC-AI-RFP-04.
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Xue, X., Gong, X., Mańdziuk, J., Yao, J., El-Alfy, ES.M., Wang, J. (2024). Theory-Guided Convolutional Neural Network with an Enhanced Water Flow Optimizer. In: Luo, B., Cheng, L., Wu, ZG., Li, H., Li, C. (eds) Neural Information Processing. ICONIP 2023. Lecture Notes in Computer Science, vol 14447. Springer, Singapore. https://doi.org/10.1007/978-981-99-8079-6_35
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DOI: https://doi.org/10.1007/978-981-99-8079-6_35
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