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New wavelet neural networks (WNN) method for linear stochastic system (StS) synthesis based on canonical expansions (CE) and mean square error (MSE) criterion is developed. Architecture of three layer WNN with one latent layer is presented. Activation functions of latent layer are based on chosen wavelet orthonormal basis with general compact carrier. Training WNN algorithm for inverse error prevalence by method of steepest descent is used. MSE optimal operator is constructed. Special formula for MSE optimal estimation of StS output in the form of linear combination of basis wavelet functions is obtained. Numerical example illustrates CE WNN preference with wavelet CE.

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Wavelet Neural Networks for Linear Stochastic System Mean Square Error Synthesis

  • 会议论文

  • 发表日期：

    2026年

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  • Igor Sinitsyn,
  • Vladimir Sinitsyn,
  • Eduard Korepanov,
  • Tatyana Konashenkova

摘要

New wavelet neural networks (WNN) method for linear stochastic system (StS) synthesis based on canonical expansions (CE) and mean square error (MSE) criterion is developed. Architecture of three layer WNN with one latent layer is presented. Activation functions of latent layer are based on chosen wavelet orthonormal basis with general compact carrier. Training WNN algorithm for inverse error prevalence by method of steepest descent is used. MSE optimal operator is constructed. Special formula for MSE optimal estimation of StS output in the form of linear combination of basis wavelet functions is obtained. Numerical example illustrates CE WNN preference with wavelet CE.