Neural network based techniques for steep behaviour represented bynonlinear advection–diffusion-reaction models

Gulen S., Sarı M., Celenk P.

Computational and Applied Mathematics, vol.44, no.6, 2025 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 44 Issue: 6
  • Publication Date: 2025
  • Doi Number: 10.1007/s40314-025-03215-w
  • Journal Name: Computational and Applied Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, Computer & Applied Sciences, zbMATH
  • Keywords: Advection–diffusion-reaction equation, Artificial neural network, Gradient descent, Particle swarm optimization
  • Yıldız Technical University Affiliated: Yes

Abstract

In this paper, a feed-forward artificial neural network (FFNN) is proposed to analyze the behaviour characterized by nonlinear advection-diffusion-reaction (ADR) equations. This approach uses a trial function that satisfies the initial and boundary conditions and depends on a neural network constructed to approximate the solution of the problem. Since the trial function contains unknown parameters, the solution process must be minimized by using efficient optimization techniques to obtain these parameters. Therefore, in this paper, the gradient descent (GD) and particle swarm optimization (PSO) techniques are proposed to address the minimization issue. The results obtained by combining artificial neural network (ANN) method with the optimization techniques have been compared and the advantages and disadvantages of the problems have been discussed. The results revealed that the proposed ANN techniques have produced accurate and reliable solutions by comparing the exact and available literature. Furthermore, these techniques are economical in terms of computational memory.