Solving Steady-State Partial Derivative Equation with Neural Network——Application to Steady-State Heat Transfer Problem

摘要：

This paper proposes to approximate the solution of Steady-state Partial Derivative Equations (SPDE) with a Feed Forward Artificial Neural Network, simply called Artificial Neural Network (ANN) in this paper. To realise this, we propose a special structure of ANN and an original way to train the ANN directly from its derivatives. The main advantage of this approximation is to obtain a solution of SPDE in form of non-linear functions (NLF). Because this solution can be easily included in VHDL-AMS models, the method is certainly a way to introduce SPDE in multi-domain simulators. To validate our method, we applied it to a two-dimension steady-state heat transfer problem. ANN approximation is compared with the high precision solution of Finite Element Method (FEM). To conclude, the method presented in this paper is simple to implement, and seems to have several applications.

关键词： heat transfer steady-state partial derivative equation VHDL-AMS feed forward neural network.

作者: Xin ZHOU Boan LIU Bruno JAMMES

作者单位: Institute of Microelectronics ,Tsinghua University, Beijing 100084, China Laboratoire d Analyse et d Architecture des Syst(e)mes (LAAS) du CNRS 7, avenue de Colonel Roche,

会议类型: 国际会议

会议名称: 8th International Conference on Neural Information Processing(ICONIP 2001)(第八届国际神经信息处理大会)

会议地点: 上海

会议语种:英文

页码: 1107-1112

在线出版日期: 2001-11-14（万方平台首次上网日期，不代表论文的发表时间）