Numerical Solution of Fractional Reaction-Diffusion Equations using an Advanced Physics-Informed Neural Network

Articles in Press

Document Type : Research Paper

Authors

Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 8415683111, Iran.

10.22034/cmde.2025.65970.3065

Abstract

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.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 01 February 2026

Files

History

  • Receive Date: 19 February 2025
  • Revise Date: 06 December 2025
  • Accept Date: 26 January 2026

Share

How to cite

Statistics