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Performing calculus operations on poorly understood engineering functions using neural networks

Published online by Cambridge University Press:  27 February 2009

Ian Flood
Ian Flood
Affiliation:
Department of Civil Engineering, University of Maryland, College Park, MD 20742, U.S.A.
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Abstract

The paper describes a novel means of performing calculus operations on poorly understood engineering functions using networks of radial Gaussian neurons. The network architecture and training algorithm used for this purpose is described briefly. Once trained, a network can be converted into a form that provides the differential or integral of the learned function, by a simple substitution of the type of activation function used at the hidden neurons. A range of substitute activation functions, for conversion to first- and second-order partial differential and integral forms of the network, are derived. Following this, the technique is tested on a selection of calculus operations for two example civil engineering problems: assessing motion in tall structures; and modeling moisture penetration in porous materials. The converted networks produced in these experiments provide accurate models of the actual differentials and integrals of the function the original networks had been taught. A method of improving the accuracy of results by training the original network beyond the region in which the converted networks operate, is described. The paper concludes by identifying some areas for further development of the technique.

Keywords

Neural NetworksPoorly Understood FunctionsCalculusRadial Gaussian Networks
Type
Articles
Information
AI EDAM , Volume 9 , Issue 5 , November 1995 , pp. 419 - 426
Copyright
Copyright © Cambridge University Press 1995

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References

REFERENCES

Chao, L.C., & Skibniewski, M.J. (1994). Estimating construction productivity: Neural network-based approach. J. Computing in Civil Eng., ASCE, 8(2), 234–251.CrossRefGoogle Scholar
Flood, I. (1991). A Gaussian-based feedforward network architecture and complementary training algorithm. Proc. Int. Joint Conf. on Neural Networks, IEEE and INNS, Vol. 1, Singapore, 171–176.Google Scholar
Flood, I., & Kartam, N. (1994). Neural networks in civil engineering. I: Principles and understanding. J. Computing in Civil Eng., ASCE, 8(2), 131–148.CrossRefGoogle Scholar
Gagarin, N., Flood, I., & Albrecht, P. (1994). Computing truck attributes with artificial neural networks. J. Computing in Civil Eng., ASCE, 8(2), 179–200.CrossRefGoogle Scholar
Gallant, A.R., & White, H. (1992). On learning the derivatives of an unknown mapping with multilayer feedforward networks. Neural Networks 5(1), 129–138.CrossRefGoogle Scholar
Hecht-Nielsen, R. (1989). Theory of the backpropagation neural network. Proc. Int. Joint Conf. on Neural Networks, Washington, DC, Vol. I, 593–605.CrossRefGoogle Scholar
Hecht-Nielsen, R. (1990). Neurocomputing. Addison-Wesley, New York.Google Scholar
Hornik, K., Stinchcombe, M., & White, H. (1990). Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks. Neural Networks 3(4), 551–560.CrossRefGoogle Scholar
Lippmann, R.P. (1987). An introduction to computing with neural nets. IEEE ASSP Magazine, 4–22.CrossRefGoogle Scholar
Rumelhart, D.E., Hinton, G.E., & Williams, R.J. (1986). Learning internal representations by error propagation. In Parallel Distributed Processing (Rumelhart, D., & McClelland, J., Eds.), Vol. 1, pp. 318–364. M.I.T. Press, Cambridge, MA.CrossRefGoogle Scholar