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Article

Solving Partial Differential Equations Using Deep Learning and Physical Constraints

by 1,2, 1,2,*, 1,2 and 1,2
1
College of Computer, National University of Defense Technology, Changsha 410073, China
2
College of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, China
*
Author to whom correspondence should be addressed.
Appl. Sci. 2020, 10(17), 5917; https://doi.org/10.3390/app10175917
Received: 31 July 2020 / Revised: 21 August 2020 / Accepted: 22 August 2020 / Published: 26 August 2020
(This article belongs to the Special Issue Applied Machine Learning)
The various studies of partial differential equations (PDEs) are hot topics of mathematical research. Among them, solving PDEs is a very important and difficult task. Since many partial differential equations do not have analytical solutions, numerical methods are widely used to solve PDEs. Although numerical methods have been widely used with good performance, researchers are still searching for new methods for solving partial differential equations. In recent years, deep learning has achieved great success in many fields, such as image classification and natural language processing. Studies have shown that deep neural networks have powerful function-fitting capabilities and have great potential in the study of partial differential equations. In this paper, we introduce an improved Physics Informed Neural Network (PINN) for solving partial differential equations. PINN takes the physical information that is contained in partial differential equations as a regularization term, which improves the performance of neural networks. In this study, we use the method to study the wave equation, the KdV–Burgers equation, and the KdV equation. The experimental results show that PINN is effective in solving partial differential equations and deserves further research. View Full-Text
Keywords: partial differential equations; deep learning; physics-informed neural network; wave equation; KdV-Burgers equation; KdV equation partial differential equations; deep learning; physics-informed neural network; wave equation; KdV-Burgers equation; KdV equation
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MDPI and ACS Style

Guo, Y.; Cao, X.; Liu, B.; Gao, M. Solving Partial Differential Equations Using Deep Learning and Physical Constraints. Appl. Sci. 2020, 10, 5917. https://doi.org/10.3390/app10175917

AMA Style

Guo Y, Cao X, Liu B, Gao M. Solving Partial Differential Equations Using Deep Learning and Physical Constraints. Applied Sciences. 2020; 10(17):5917. https://doi.org/10.3390/app10175917

Chicago/Turabian Style

Guo, Yanan, Xiaoqun Cao, Bainian Liu, and Mei Gao. 2020. "Solving Partial Differential Equations Using Deep Learning and Physical Constraints" Applied Sciences 10, no. 17: 5917. https://doi.org/10.3390/app10175917

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