A discretization-free deep neural network-based approach for advection-dispersion-reaction mechanisms

Hande Uslu Tuna, Murat Sari, Tahir Cosgun*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This study aims to provide insights into new areas of artificial intelligence approaches by examining how these techniques can be applied to predict behaviours for difficult physical processes represented by partial differential equations, particularly equations involving nonlinear dispersive behaviours. The current advection-dispersion-reaction equation is one of the key formulas used to depict natural processes with distinct characteristics. It is composed of a first-order advection component, a third-order dispersion term, and a nonlinear response term. Using the deep neural network approach and accounting for physics-informed neural network awareness, the problem has been elaborately discussed. Initial and boundary conditions are added as constraints when the neural networks are trained by minimizing the loss function. In comparison to the existing results, the approach has produced qualitatively correct kink and anti-kink solutions, with losses often remaining around 0.01%. It has also outperformed several traditional discretization-based methods.

Original languageEnglish
Article number076006
JournalPhysica Scripta
Issue number7
Publication statusPublished - 1 Jul 2024

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  • advection-dispersion-reaction model
  • kink waves
  • physics-informed deep neural networks
  • solitary waves


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