Orthogonal Embedding-Based Artificial Neural Network Solutions to Ordinary Differential Equations

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

Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi
Cilt: 25 Sayı: 3
Orthogonal Embedding-Based Artificial Neural Network Solutions to Ordinary Differential Equations

Orthogonal Embedding-Based Artificial Neural Network Solutions to Ordinary Differential Equations

Authors : Tolga Recep Uçar, Hasan Halit Tali

Pages : 489-496

Doi:10.35414/akufemubid.1558289

View : 103 | Download : 86

Publication Date : 2025-06-10

Article Type : Research Paper

Abstract :Providing numerical solutions to differential equations in cases where analytical solutions are not available is of great importance. Recently, obtaining more accurate numerical solutions with artificial neural network-based machine learning methods are seen as promising developments for numerical solutions of differential equations. In this paper, a low-cost, orthogonal embedding-based network with fast training by simple gradient descent algorithm is proposed to obtain numerical solutions of differential equations. This architecture is essentially a two-layer neural network that takes orthogonal polynomials as input. The efficiency and accuracy of the method used in this paper are demonstrated in various problems and comparisons are made with other methods. It is observed that the proposed method stands out especially when compared with high-cost solutions.
Keywords : Doğrusal olmayan adi diferansiyel denklemler, nümerik yaklaşım, yapay sinir ağları, ortogonal polinomlar

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.