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In this paper, a new Logistic Basis Function Neural Network (LBFNN) algorithm is proposed and applied to solve Fokker–Planck–Kolmogorov (FPK) equations for stochastic dynamical systems under random excitation. Our attention is focused on the transient solution of the systems under Non-Gaussian excitation. Firstly, we built a neural network by using Logistic probability functions as the basis functions, in which the weighted coefficients are unknown and to be determined. After that, considering the constraint from FPK equation and the normalization condition from the weighted parameters, we construct the loss function to be comprised by these two parts. The innovation of our algorithm is that unknown weighted parameters in LBFNN can be obtained by solving a set of algebraic iteration formulas instead of testify by sample data. Results show that LBFNN algorithm is capable to get transient solutions of the systems under Non-Gaussian excitation. Monte-carlo simulation are utilized in order to examine the accuracy of the LBFNN algorithm. The good agreements in different comparisons demonstrate the validity and the strength of the LBFNN algorithm.

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Solving FPK Equations for Stochastic Dynamical Systems Under Non-Gaussian Excitation by Logistic-Based Neural Network

  • 会议论文

  • 发表日期：

    2025年

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  • Wei Li,
  • Yu Guan,
  • Mingzhi Lin

摘要

In this paper, a new Logistic Basis Function Neural Network (LBFNN) algorithm is proposed and applied to solve Fokker–Planck–Kolmogorov (FPK) equations for stochastic dynamical systems under random excitation. Our attention is focused on the transient solution of the systems under Non-Gaussian excitation. Firstly, we built a neural network by using Logistic probability functions as the basis functions, in which the weighted coefficients are unknown and to be determined. After that, considering the constraint from FPK equation and the normalization condition from the weighted parameters, we construct the loss function to be comprised by these two parts. The innovation of our algorithm is that unknown weighted parameters in LBFNN can be obtained by solving a set of algebraic iteration formulas instead of testify by sample data. Results show that LBFNN algorithm is capable to get transient solutions of the systems under Non-Gaussian excitation. Monte-carlo simulation are utilized in order to examine the accuracy of the LBFNN algorithm. The good agreements in different comparisons demonstrate the validity and the strength of the LBFNN algorithm.