神经网络的空间分解方法求解热传导方程

Space compartment method for solving steady-state heat transfer problem with neural networks

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。

Micro-Electro-Mechanical System (MEMS) simulations and, more generally, multi-domain system simulations need to solve partial derivative equations (PDE). This paper describes a method to approximate the analytical solution of the PDE using artificial neural networks (ANN). The operating area is compartmentalized into several areas with different neural networks used to approximate the solution in each area. The accuracy is much better and the training time is reduced to less than 1/10 of the method without space compartment. A very precise solution was obtained for the steady-state heat transfer equation as an example. Since this solution can be easily included in VHDL-AMS (VHSIC hardware description language-analog and mixed-signal) models, the method is an effective way to introduce PDE solutions into multi-domain simulators.