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

USLU TUNA H., Sarı M., Cosgun T.

Physica Scripta, cilt.99, sa.7, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 99 Sayı: 7
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1088/1402-4896/ad5258
  • Dergi Adı: Physica Scripta
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Chemical Abstracts Core, Compendex, INSPEC, zbMATH
  • Anahtar Kelimeler: advection-dispersion-reaction model, kink waves, physics-informed deep neural networks, solitary waves
  • Yıldız Teknik Üniversitesi Adresli: Evet

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.