An Application of Improved Neural Networks to Solve Differetial Equation based Z-Process

Document Type : Research Article

Authors

1 Department of Mathematics, N.T.C., Islamic Azad University, Tehran, Iran,

2 2Department of Mathematics, C.T.C, Islamic Azad University, Tehran, Iran

3 3Department of Mathematics, Ker. C., Islamic Azad University, Kermanshah, Iran

4 Department of Mathematics, Faculty of Basic Sciences Imam Ali University, Tehran, Iran

10.22080/frai.2025.5666

Abstract

In this work, we utilize a modified neural network to introduce a new method for solving the differential equation with Z-number initial value estimation. The proposed method consists of a function evaluating Z-numbers. The generalized neural network consists of three layers. The first layer contains input, weights of the first layer and bias of the neural network. So that, the number of weights (Corresponding to the number of equations of the main problem) corresponds to the number of inputs. The second layer contains neurons and nonlinear transmission functions. The third layer, which is the same output layer, consists of an output, linear transmission functions and weights of the last layer. Note that an improved neural network inputs are real based on which its weights and outputs are Z-valuation. In this matter, in order to train the improved neural network, we consider the objective function of the neural network to be the same as the sum squared error function. We minimize the target function to obtain the weights of the neural network using an optimization technique. Finally, the value obtained from the proposed method converges to the value of the original solution. In order to prove that the proposed method is a suitable and practical method for the exact solution approximation, we present two numerical examples as well.

Keywords

References

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Future Research on AI and IoT
Volume 1, Issue 2
August 2025
Pages 12-18

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History

  • Receive Date: 17 July 2025
  • Accept Date: 05 August 2025
  • First Publish Date: 05 August 2025
  • Publish Date: 01 August 2025

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