Utilizing symmetry-enhanced physics-informed neural network to obtain the solution beyond sampling domain for partial differential equations
Author:
Publisher
Springer Science and Business Media LLC
Subject
Electrical and Electronic Engineering,Applied Mathematics,Mechanical Engineering,Ocean Engineering,Aerospace Engineering,Control and Systems Engineering
Link
https://link.springer.com/content/pdf/10.1007/s11071-023-08975-w.pdf
Reference41 articles.
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2. Han, J., Jentzen, A., Epriya, W.N.: Solving high-dimensional partial differential equations using deep learning. Proc. Natl. Acad. Sci. 115(34), 8505–8510 (2018)
3. 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)
4. Yu, J., Lu, L., Meng, X., Karniadakis, G.E.: Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems. Comput. Methods Appl. Mech. Engrg. 393, 114823 (2022)
5. Li, J., Chen, J., Li, B.: Gradient-optimized physics-informed neural networks (GOPINNs): a deep learning method for solving the complex modified KdV equation. Nonlinear Dyn. 107, 781–792 (2022)
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