NDLI: Neural Network Method for Solving Partial Differential Equations

Content Provider	Springer Nature Link
Author	Aarts, Lucie P. van der Veer, Peter
Copyright Year	2001
Abstract	A method is presented to solve partial differential equations (pde's) and its boundary and/or initial conditions by using neural networks. It uses the fact that multiple input, single output, single hidden layer feedforward networks with a linear output layer with no bias are capable of arbitrarily well approximating arbitrary functions and its derivatives, which is proven by a number of authors and well known in literature. Knowledge about the pde and its boundary and/or initial conditions is incorporated into the structures and the training sets of several neural networks. In this way we obtain networks of which some are specifically structured. To find the solution of the pde and its boundary and/or initial conditions we have to train all obtained networks simultaneously. Therefore we use an evolutionary algorithm to train the networks. We demonstrate the working of our method by applying it to two problems.
Starting Page	261
Ending Page	271
Page Count	11
File Format	PDF
ISSN	13704621
Journal	Neural Processing Letters
Volume Number	14
Issue Number	3
e-ISSN	1573773X
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2001-01-01
Publisher Place	Boston
Access Restriction	Subscribed
Subject Keyword	Artificial Intelligence (incl. Robotics) Nonlinear Dynamics, Complex Systems, Chaos, Neural Networks Electronic and Computer Engineering Operation Research/Decision Theory
Content Type	Text
Resource Type	Article
Subject	Neuroscience Artificial Intelligence Computer Networks and Communications Software

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