Study on Numerical Solutions to Hyperbolic Partial Differential Equations Based on the Convolutional Neural Network Model

GAO Puyang; ZHAO Zitong; YANG Yang

doi:10.21656/1000-0887.420050

Volume 42 Issue 9

Sep. 2021

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GAO Puyang, ZHAO Zitong, YANG Yang. Study on Numerical Solutions to Hyperbolic Partial Differential Equations Based on the Convolutional Neural Network Model[J]. Applied Mathematics and Mechanics, 2021, 42(9): 932-947. doi: 10.21656/1000-0887.420050

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Study on Numerical Solutions to Hyperbolic Partial Differential Equations Based on the Convolutional Neural Network Model

doi: 10.21656/1000-0887.420050

1. School of Sciences, Chang’an University, Xi’an 710064, P.R.China;
2. School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072, P.R.China

Funds:

The National Natural Science Foundation of China(11901051

11971075)

Received Date: 2021-02-23
Rev Recd Date: 2021-04-21

Available Online: 2021-09-29

Abstract

Abstract

In recent years, artificial neural networks developed rapidly. Application of this method to partial differential equations became a new idea for exploring numerical solutions to differential equations. Compared with the traditional methods, it has some advantages, such as a wide range of applications (i.e. the same model can be used to solve multiple types of equations) and low meshing requirements. In addition, the trained model can be directly used to calculate the numerical solution at any point in the computation domain. The weight coefficients in the traditional finite volume method were optimized based on the convolutional neural network model to get a new numerical scheme with highresolution results on the coarse grid. The proposed model helps solve the Burgers and level set equations efficiently and stably with high accuracy.
- convolutional neural network model,
- Burgers equation,
- level set equation,
- finite volume method

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References(19)

References

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