Physics Informed Neural Network Method For the Numerical Solution of Fractional Diffusion Equations

Home Page
About
Submit A Journal
Submit A Conference
Submit Paper/Book
- Submit a Preprint
- Submit a Book
Contact

Erzincan Üniversitesi Fen Bilimleri Enstitüsü Dergisi
Cilt: 18 Sayı: 3
Physics Informed Neural Network Method For the Numerical Solution of Fractional Diffusion Equations

Physics Informed Neural Network Method For the Numerical Solution of Fractional Diffusion Equations

Authors : Mehmet Fatih Uçar, Burcu Ece Alp

Pages : 726-734

View : 123 | Download : 284

Publication Date : 2025-12-31

Article Type : Research Paper

Abstract :Artificial neural networks are increasingly used to construct continuous solution functions for solving various kinds of differential equations. In this study, we propose a physics informed neural network (PINN) method to solve fractional diffusion equations with variable coefficients on a finite domain. The PINN generate approximate solutions to the fractional PDE by training to minimize the physical loss function consisting of residual, boundary condition and initial condition parts. Fractional PDE is discretized with the Grunwald-Letnikov formula and the resulted semi-discrete equation is used to construct the residual function of the PINN. Numerical experiments show that the present PINN method provides accurate solutions on the considered computational space-time domain.
Keywords : Kesirli Difüzyon Denklemi, PINN Metodu, Nümerik Yöntemler

ORIGINAL ARTICLE URL

* There may have been changes in the journal, article,conference, book, preprint etc. informations. Therefore, it would be appropriate to follow the information on the official page of the source. The information here is shared for informational purposes. IAD is not responsible for incorrect or missing information.