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Ahmadkhanpour, Fatemeh, Kheiri, Hossein, Azarmir, Nima, Modarres Khiyabani, Farzin. (1403). Solving initial value problems using multilayer perceptron artificial neural networks. سامانه مدیریت نشریات علمی, 13(1), 13-24. doi: 10.22034/cmde.2024.58774.2486
Fatemeh Ahmadkhanpour; Hossein Kheiri; Nima Azarmir; Farzin Modarres Khiyabani. "Solving initial value problems using multilayer perceptron artificial neural networks". سامانه مدیریت نشریات علمی, 13, 1, 1403, 13-24. doi: 10.22034/cmde.2024.58774.2486
Ahmadkhanpour, Fatemeh, Kheiri, Hossein, Azarmir, Nima, Modarres Khiyabani, Farzin. (1403). 'Solving initial value problems using multilayer perceptron artificial neural networks', سامانه مدیریت نشریات علمی, 13(1), pp. 13-24. doi: 10.22034/cmde.2024.58774.2486
Ahmadkhanpour, Fatemeh, Kheiri, Hossein, Azarmir, Nima, Modarres Khiyabani, Farzin. Solving initial value problems using multilayer perceptron artificial neural networks. سامانه مدیریت نشریات علمی, 1403; 13(1): 13-24. doi: 10.22034/cmde.2024.58774.2486

Solving initial value problems using multilayer perceptron artificial neural networks

Computational Methods for Differential Equations
مقاله 2، دوره 13، شماره 1، فروردین 2025، صفحه 13-24    اصل مقاله (561.09 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.58774.2486
نویسندگان
Fatemeh Ahmadkhanpour1؛ Hossein Kheiri* 2؛ Nima Azarmir1؛ Farzin Modarres Khiyabani1
1Department of Mathematics, Faculty of Science, Tabriz Branch, Islamic Azad University, Tabriz, Iran.
2Department of Applied Mathematics, Faculty of Mathematics, Statistics and Computer Science, University of Tabriz, Tabriz, Iran.
چکیده
This research introduces a novel approach using artificial neural networks (ANNs) to tackle ordinary differential equations (ODEs) through an innovative technique called enhanced back-propagation (EBP). The ANNs adopted in this study, particularly multilayer perceptron neural networks (MLPNNs), are equipped with tunable parameters such as weights and biases. The utilization of MLPNNs with universal approximation capabilities proves to be advantageous for ODE problem solving. By leveraging the enhanced back-propagation algorithm, the network is fine-tuned to minimize errors during unsupervised learning sessions. To showcase the effectiveness of this method, a diverse set of initial value problems for ODEs are solved and the results are compared against analytical solutions and conventional techniques, demonstrating the superior performance of the proposed approach.
کلیدواژه‌ها
Artificial neural networks؛ Ordinary differential equations؛ Back-propagation algorithm
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