A precise integration method for dynamic equations based on dual neural networks
YANG Yong1,LI Haibin1,2
1. School of Science, Inner Mongolia University of Technology, Hohhot 010051, China;
2. Engineering Training Center , Inner Mongolia University of Technology, Hohhot 010051, China
Abstract:For dynamics equation, the existing common solution method is the precise integration method, but the result of the equation given by the precise integration method contains complex integrals, which is difficult to solve by the traditional numerical integration method. In this manuscript, an integration algorithm is proposed based on neural networks. The algorithm builds two neural networks, one neural network is used to approximate the integral function and the other neural network is used to approximate the original function. While one neural network is trained, the other neural network is trained at the same time. The result of the integration can then be obtained by Newton Leibniz function. The algorithm of this manuscript takes advantage of the function fitting of the neural network, which is insensitive to the selected time step during the solution of the kinetic equations, does not require the inverse of the matrix, and does not require the assumption of inhomogeneous term. With computational examples, the algorithm of this manuscript is compared with a variety of existing commonly used methods. The calculation results show that the method has high accuracy and wide applicability.
Key words: high precision integration; dual neural networks; dynamic equation; direct integral
杨永1,李海滨1,2. 基于对偶神经网络的动力方程精细积分法[J]. 振动与冲击, 2022, 41(16): 188-193.
YANG Yong1,LI Haibin1,2. A precise integration method for dynamic equations based on dual neural networks. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(16): 188-193.
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