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| Application of machine learning in solving one-dimensional hyperbolic conservation law equation |
| Received:March 09, 2021 Revised:April 16, 2021 |
| View Full Text View/Add Comment Download reader |
| DOI：10.7511/jslx20210309001 |
| KeyWord:hyperbolic conservation law equation machine learning BP neural network entropy stable scheme adaptive moving grid |
| Author | Institution |
| 赵青宇 |
长安大学 理学院, 西安 |
| 郑素佩 |
长安大学 理学院, 西安 |
| 李霄 |
长安大学 理学院, 西安 |
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| Abstract: |
| The hyperbolic conservation equation is of great significance in the calculation of aerodynamics,physics,oceanography and many other fields.In this paper,the BP neural network based on a machine learning framework is applied to solve the hyperbolic conservation equation approximately.First of all,the algorithm constructs the network input from the numerical solutions of multiple time layers obtained from the entropy stable scheme and based on the adaptive moving grid,and uses the numerical solution of the corresponding multiple time layers obtained by the high-resolution entropy stable scheme to construct the network output,and the data set is normalized.Then,using the training data of three-layer BP neural network,the neural network with good performance is obtained,so as to realize the prediction of the numerical solutions at any given time level node.Finally,five numerical examples show that the algorithm is suitable for solving this kind of problems,and it has high resolution with no physical oscillations. |
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