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Solving Initial Value Problems Using Multilayer Perceptron Artificial Neural Networks | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 08 اردیبهشت 1403 اصل مقاله (1.27 M) | ||
| 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. | ||
| 2Faculty of Mathematical Sciences, 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 &lrm | ||
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آمار تعداد مشاهده مقاله: 47 تعداد دریافت فایل اصل مقاله: 89 |
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