Paper on Neuroprose: Solution of Nonlinear ODEs

[Andrew Meade 238Cox x4906]

FTP-host: archive.cis.ohio-state.edu
FTP-file: pub/neuroprose/meade.nonlinearodes.ps.Z

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The following paper has been placed in the Neuroprose archive at 
Ohio State University: 

"Solution of Nonlinear Ordinary Differential Equations 
 by Feedforward Neural Networks"
 A.J. Meade, Jr. and A.A. Fernandez 

(25 pages. No hard copies available.) 

To appear in Mathematical and Computer Modelling 


ABSTRACT:
It is demonstrated, through theory and numerical examples, 
how it is possible to directly construct a feedforward neural 
network to approximate nonlinear ordinary differential equations 
without the need for training. The method, utilizing a piecewise 
linear map as the activation function, is linear in storage, and 
the $L_2$ norm of the network approximation error 
decreases monotonically with the increasing number of hidden 
layer neurons. 

The construction requires imposing certain constraints on the values 
of the input, bias, and output weights, and the attribution 
of certain roles to each of these parameters. 
All results presented used the piecewise linear activation function. 
However, the presented approach should also be applicable to the use of 
hyperbolic tangents, sigmoids, and radial basis functions. 


Andrew J. Meade, Jr. and Alvaro A. Fernandez 
Rice University 
Department of Mechanical Engineering 
and Materials Science 
Mail Stop 321 
Houston, Texas, 77251-1892, USA 
Phone: (713) 527-8101 ext. 3590 
email: meade at rice.edu 
 
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Retrieve this paper by anonymous ftp:

unix> ftp archive.cis.ohio-state.edu (or 128.146.8.52)
    Name: anonymous
    Password: <your e-mail address>
    ftp> cd pub/neuroprose
    ftp> binary
    ftp> get meade.nonlinearodes.ps.Z 
    ftp> quit
unix> uncompress meade.nonlinearodes.ps.Z 

Thanks to Jordan Pollack for maintaining this archive. 

A.J. Meade