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Numerical Solution of Fractional Reaction-Diffusion Equations using an Advanced Physics-Informed Neural Network | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 12 بهمن 1404 اصل مقاله (1.91 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22034/cmde.2025.65970.3065 | ||
| نویسندگان | ||
| Maryam Mohammadi؛ Reza Mokhtari* ؛ Mohadese Ramezani | ||
| Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 8415683111, Iran. | ||
| چکیده | ||
| This paper introduces an innovative approach featuring an advanced Physics-Informed Neural Network (PINN) that effectively tackles the challenges associated with fractional reaction-diffusion problems. These problems often pose difficulties for traditional numerical methods, especially in high-dimensional spaces or complex geometries. By employing a suitable auxiliary function, the approximate solution automatically satisfies the exact boundary conditions, further enhancing the method's efficiency and accuracy. Additionally, the proposed model can handle weak singularities in the solution, which are common in fractional models, making it particularly well-suited for more challenging cases. We conducted numerical experiments to demonstrate the effectiveness of the proposed framework. The results indicate that this framework significantly improves the performance of radial basis function neural networks, making them better suited for handling complex fractional models across different geometric configurations. | ||
| کلیدواژهها | ||
| fractional PINN؛ fractional reaction-diffusion equations؛ weak singular solution؛ auxiliary function | ||
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آمار تعداد مشاهده مقاله: 30 تعداد دریافت فایل اصل مقاله: 78 |
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