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

Hande Uslu Tuna, Murat Sari, Tahir Cosgun*

*Bu çalışma için yazışmadan sorumlu yazar

Araştırma sonucu: Dergiye katkıMakalebilirkişi

Özet

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.

Orijinal dilİngilizce
Makale numarası076006
DergiPhysica Scripta
Hacim99
Basın numarası7
DOI'lar
Yayın durumuYayınlandı - 1 Tem 2024

Bibliyografik not

Publisher Copyright:
© 2024 IOP Publishing Ltd.

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