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在微机电系统(MEMS)等众多领域的模拟中,都需要求解偏微分方程。常用的方法得到的都是数值形式的解。该文提出了一种利用人工神经网络得到偏微分方程的解析形式解的方法。把神经网络的工作区域划分为小的区域,用不同的神经网络逼近,计算精度提高了一倍,计算时间减少到十分之一以下。用它求解了二维空间上的静态热传导问题,得到了精确的解析形式的解。因为这种解可以方便地用于VHDL-AMS(VHSIChardwaredescriptionlanguage-analogandmixed-signal)模型,所以它可以用于各个领域的偏微分方程的模拟。
In many fields such as microelectromechanical systems (MEMS) simulation, the need to solve partial differential equations. Commonly used methods give numerical solutions. In this paper, we propose a method to obtain the analytic formal solution of partial differential equations by means of artificial neural network. The work area of neural network is divided into small areas, with different neural network approximation, the calculation accuracy is doubled, the calculation time is reduced to less than one-tenth. It is used to solve the problem of static heat conduction in two-dimensional space, and the exact analytical solution is obtained. Because this solution can be conveniently used in VHDL-AMS (VHSIChardwaredescriptionlanguage-analogandmixed-signal) model, it can be used in the simulation of PDEs in various fields.