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	Space compartment method for solving partial derivative equation with neural networks - application to steady-state heat transfer problem
	Zhou Xin ; Liu Boan ; Shi Bingxue
	2010-05-07 ; 2010-05-07
关键词	Application Practical Theoretical or Mathematical/ approximation theory feedforward neural nets hardware description languages heat transfer learning (artificial intelligence) mixed analogue-digital integrated circuits nonlinear functions partial differential equations/ space compartment method steady state partial derivative equations steady state heat transfer problem feedforward artificial neural networks ANN training nonlinear functions multidomain simulators VHDL-AMS models approximation theory/ A4725Q Convection and heat transfer A0230 Function theory, analysis A0260 Numerical approximation and analysis B1280 Mixed analogue-digital circuits B1295 Neural nets (circuit implementations) B0290P Differential equations (numerical analysis) B0290K Nonlinear and functional equations (numerical analysis) B0290F Interpolation and function approximation (numerical analysis) C5190 Neural net devices C1230L Learning in AI C4170 Differential equations (numerical analysis) C4150 Nonlinear and functional equations (numerical analysis) C4130 Interpolation and function approximation (numerical analysis)
中文摘要	A new method is presented to approximate the solution of steady-state partial derivative equations (SPDE) with feedforward artificial neural networks (ANN) in this paper. To realize this, we propose a special structure of ANN and an original way to train the ANN directly from its derivatives, and decompose the operating area into several ones. The main advantage of this approximation is to obtain a solution of SPDE in the form of non-linear functions (NLF). Since 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).
语种	英语 ; 英语
出版者	Chinese Inst. Electron ; China
内容类型	期刊论文
源URL	[http://hdl.handle.net/123456789/16537]
专题	清华大学
推荐引用方式 GB/T 7714	Zhou Xin,Liu Boan,Shi Bingxue. Space compartment method for solving partial derivative equation with neural networks - application to steady-state heat transfer problem[J],2010, 2010.
APA	Zhou Xin,Liu Boan,&Shi Bingxue.(2010).Space compartment method for solving partial derivative equation with neural networks - application to steady-state heat transfer problem..
MLA	Zhou Xin,et al."Space compartment method for solving partial derivative equation with neural networks - application to steady-state heat transfer problem".(2010).

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