连续Hopfield网络在热传导有限元计算中的应用

Application of continuous Hopfield network in heat exchange computing with finite element method

连续Hopfield网络是一个能收敛的稳定网络,如果一个系统的优化问题可以用"能量函数"作为目标函数,则总可以用连续Hopfield网络对其进行求解。依据热传导有限元特点,将有限元计算问题转化为带约束的非线性优化问题,找出了优化目标函数,并给出求解该问题的改进Hopfield(TH)网络;最后对一个简单温度场神经计算进行数值仿真,仿真结果表明连续Hopfield神经网络能完成有限元模型的求解。

Continuous Hopfiled network is a convergent neural network. If the ＂Energy Function＂ can be used as the target function of a system＇ s optimizing problem, then Hopfiled network can always find out the result of the problem. Based on analyzing the characteristic of heat exchange with finite element method, the finite element computing problem is changed into a nonlinear optimizing problem with re- striction, and the Hopfield neural network with a target function for optimizing computing is given. Fi- nally, a simulation about simple temperature field with the neural network is carried out. The result of simulation shows that continuous Hopfiled neural network can apply to finite element model＇ s resolving.