Physics-informed neural networks in iterative form of nonlinear equations for numerical algorithms and simulations of delay differential equations

Jilong He and Tiamiyu, Abd’gafar Tunde

Physica A: Statistical Mechanics and its Applications, 2025, vol. 660, issue C

Abstract: This paper proposes a new high-precision and efficient algorithm for solving delay differential equations using a physics-informed neural network. We utilize initial conditions and two types of neural network methods, namely the Extreme Learning Machine and the Multilayer Perceptron, to construct trial functions that accurately satisfy the initial conditions. These trial functions are then used to discretize the delay differential equations. In contrast to the original physics-informed neural network, we employ an iterative approach by transforming the form of the loss function into an algebraic system generated at configuration points. The algebraic system is iteratively computed to obtain the optimal parameters, which correspond to the optimal solution of the equation. Finally, we validate the effectiveness of our method through six numerical examples, including complex delay differential systems, demonstrating that our approach yields high-precision and efficient numerical results.

Keywords: Delay differential equations; Physics-informed neural networks; Trial function system of nonlinear equations; Iterative optimization; Numerical simulation (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437125000202
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:660:y:2025:i:c:s0378437125000202

DOI: 10.1016/j.physa.2025.130368

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().