针对一般动力学方程，提出了一种用于求解具有任意非齐次项动力学方程的对偶神经网络精细积分算法。在时间域内，对动力学非齐次方程求解中涉及到的积分运算，选用一组神经网络同时逼近被积函数和原函数，然后通过牛顿莱布尼茨公式实现积分项的求解。该方法利用神经网络的函数拟合优势，具有对时间步长不敏感，不需要对矩阵求逆，不对非齐次项进行假设等优点。通过算例与精细积分法、威尔逊- 、广义精细积分法等方法进行比较，计算结果表明该方法精度较高，适用范围广。
关键词：精细积分法；对偶神经网络 ；动力方程；直接积分
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
关键词
精细积分法 /
对偶神经网络 /
动力方程 /
直接积分
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Key words
high precision integration /
dual neural networks /
dynamic equation /
direct integral
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