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Volterra models and three-layer perceptrons.

V Z Marmarelis1, X Zhao

  • 1Dept. of Biomed. Eng., Univ. of Southern California, Los Angeles, CA.

IEEE Transactions on Neural Networks
|January 1, 1997
PubMed
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This study introduces separable Volterra networks (SVNs), a type of artificial neural network, to effectively model high-order Volterra systems. SVNs overcome the computational limits of traditional discrete-time Volterra models (DVMs), enabling practical analysis of complex nonlinear systems.

Area of Science:

  • Nonlinear System Modeling
  • Artificial Intelligence
  • Computational Neuroscience

Background:

  • Discrete-time Volterra models (DVMs) are crucial for analyzing nonlinear physical and physiological systems but are computationally limited to low-order nonlinearities.
  • Estimating high-order kernels in DVMs is often infeasible due to computational constraints.
  • Three-layer perceptrons (TLPs) possess the capability to represent arbitrary-order nonlinear input-output mappings.

Purpose of the Study:

  • To propose a novel approach for practical modeling of high-order Volterra systems using artificial neural networks.
  • To explore the relationship between DVMs and TLPs for nonlinear system modeling.
  • To introduce separable Volterra networks (SVNs) as a viable solution for overcoming DVM limitations.

Main Methods:

Related Experiment Videos

  • Investigated the relationship between DVMs and TLPs with tapped-delay inputs.
  • Introduced and utilized a variant of TLPs with polynomial activation functions, termed separable Volterra networks (SVNs).
  • Demonstrated DVM estimation via SVN training using backpropagation and compared with the Laguerre expansion technique (LET).

Main Results:

  • Established explicit relations between DVMs and SVNs.
  • Developed practicable models for highly nonlinear systems using SVNs from stimulus-response data.
  • Showcased the feasibility of SVN-based DVM estimation through simulations, outperforming LET in certain aspects.

Conclusions:

  • Separable Volterra networks (SVNs) provide a practical method for modeling high-order Volterra systems, overcoming the computational limitations of traditional DVMs.
  • SVNs offer an effective alternative for analyzing complex nonlinear systems where DVMs fall short.
  • The proposed SVN approach facilitates more comprehensive analysis of nonlinear phenomena in various scientific domains.