<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>In order to study the application of nonlinear fractional differential equations in computer artificial intelligence algorithms. First, the concept, properties and commonly used neural network models of artificial neural network are introduced, the domestic and foreign status quo of the application of fractional calculus theory to neural network technology is described. Then, the definition, properties and numerical calculation methods of fractional calculus theory are introduced in detail. Then, based on the analysis of artificial intelligence neural network algorithm, the theory of fractional differentiation is introduced, construct BP neural network based on fractional order theory. The Sigmoid function is used as the node function of the neural network, and the actual data is used as the sample set, train a fractional-order network. Finally, by training the network, summarize the change of the two parameters a and p in the function, the impact on the training of the entire network, and make a simple comparison with the fractional order neural network based on the sigmoid function. Experiments show that a variable-order iterative learning algorithm is proposed and applied to the training of neural networks, the results show the feasibility of this algorithm and its advantages in convergence speed and convergence accuracy.</p>
</abstract>

In order to study the application of nonlinear fractional differential equations in computer artificial intelligence algorithms. First, the concept, properties and commonly used neural network models of artificial neural network are introduced, the domestic and foreign status quo of the application of fractional calculus theory to neural network technology is described. Then, the definition, properties and numerical calculation methods of fractional calculus theory are introduced in detail. Then, based on the analysis of artificial intelligence neural network algorithm, the theory of fractional differentiation is introduced, construct BP neural network based on fractional order theory. The Sigmoid function is used as the node function of the neural network, and the actual data is used as the sample set, train a fractional-order network. Finally, by training the network, summarize the change of the two parameters a and p in the function, the impact on the training of the entire network, and make a simple comparison with the fractional order neural network based on the sigmoid function. Experiments show that a variable-order iterative learning algorithm is proposed and applied to the training of neural networks, the results show the feasibility of this algorithm and its advantages in convergence speed and convergence accuracy.

Application of Nonlinear Fractional Differential Equations in Computer Artificial Intelligence Algorithms

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

In order to study the application of nonlinear fractional differential equations in computer artificial intelligence algorithms. First, the concept, properties...

Application of Nonlinear Fractional Differential Equations in Computer Artificial Intelligence Algorithms

Online veröffentlicht: 15. Juli 2022

Seitenbereich: 1145 - 1154

Eingereicht: 19. Feb. 2022

Akzeptiert: 25. Apr. 2022

DOI: https://doi.org/10.2478/amns.2022.2.0101

Schlüsselwörter
Nonlinear, Fractional differential equation, Artificial intelligence algorithm

© 2023 Jue Xie et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1

Figure 2

Figure 3

Application of Nonlinear Fractional Differential Equations in Computer Artificial Intelligence Algorithms

Online veröffentlicht: 15. Juli 2022

Seitenbereich: 1145 - 1154

Eingereicht: 19. Feb. 2022

Akzeptiert: 25. Apr. 2022

DOI: https://doi.org/10.2478/amns.2022.2.0101

SchlüsselwörterNonlinear, Fractional differential equation, Artificial intelligence algorithm

© 2023 Jue Xie et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1

Figure 2

Figure 3

Schlüsselwörter
Nonlinear, Fractional differential equation, Artificial intelligence algorithm