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Model order reduction using neural network principal component analysis and generalized dimensional analysis

F.H. Bellamine (The National Institute of Applied Sciences and Technology in Tunis,Tunis Cedex, Tunisia and University of Waterloo, Waterloo, Canada)
A. Elkamel (University of Waterloo, Waterloo, Canada)

Engineering Computations

ISSN: 0264-4401

Article publication date: 18 July 2008



This paper seeks to present a novel computational intelligence technique to generate concise neural network models for distributed dynamic systems.


The approach used in this paper is based on artificial neural network architectures that incorporate linear and nonlinear principal component analysis, combined with generalized dimensional analysis.


Neural network principal component analysis coupled with generalized dimensional analysis reduces input variable space by about 90 percent in the modeling of oil reservoirs. Once trained, the computation time is negligible and orders of magnitude faster than any traditional discretisation schemes such as fine‐mesh finite difference.

Practical implications

Finding the minimum number of input independent variables needed to characterize a system helps in extracting general rules about its behavior, and allows for quick setting of design guidelines, and particularly when evaluating changes in the physical properties of systems.


The methodology can be used to simulate dynamical systems characterized by differential equations, in an interactive CAD and optimization providing faster on‐line solutions and speeding up design guidelines.



Bellamine, F.H. and Elkamel, A. (2008), "Model order reduction using neural network principal component analysis and generalized dimensional analysis", Engineering Computations, Vol. 25 No. 5, pp. 443-463.



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