Modelling the dynamics of nonlinear partial differential equations using neural networks

DOI10.1016/j.cam.2003.12.045zbMath1049.65108OpenAlexW2065400254MaRDI QIDQ596178

Suad Al-Enezi, Nejib Smaoui

Publication date: 10 August 2004

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2003.12.045

zbMATH Keywords

Navier-Stokes equationsnumerical examplesNeural networksbifurcationsymmetriesKarhunen-Loeve decompositionOne-dimensional Kuramoto-Sivashinsky equationpseudospectral Galerkin methodTwo-dimensional

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Navier-Stokes equations for incompressible viscous fluids (76D05) Dynamical systems in fluid mechanics, oceanography and meteorology (37N10) Navier-Stokes equations (35Q30) Dynamical aspects of symmetries, equivariant bifurcation theory (37G40) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

Related Items (4)

Metric-based, goal-oriented mesh adaptation using machine learning ⋮ Multilayer perceptrons and radial basis function neural network methods for the solution of differential equations: a survey ⋮ Solving initial-boundary value problems for systems of partial differential equations using neural networks and optimization techniques ⋮ Projection-based and neural-net reduced order model for nonlinear Navier-Stokes equations

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