Machine Learning Modeling for Shape Parameter c in MQ-RBF Applied to Burgers’ Equations

Pekmen B., Kayabasi M.

International Conference on Intelligent and Fuzzy Systems, INFUS 2024, Çanakkale, Türkiye, 16 - 18 Temmuz 2024, cilt.1088 LNNS, ss.294-301 identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası: 1088 LNNS
  • Doi Numarası: 10.1007/978-3-031-70018-7_32
  • Basıldığı Şehir: Çanakkale
  • Basıldığı Ülke: Türkiye
  • Sayfa Sayıları: ss.294-301
  • Anahtar Kelimeler: Burgers’ equations, multiquadric, neural networks, radial basis function, shape parameter
  • TED Üniversitesi Adresli: Evet

Özet

The main goal of this study is to model the shape parameter of multiquadric radial basis function (RBF) by using neural networks. The data for modeling is obtained from the numerical results. The one and the two dimensional Burgers’ equations are numerically concerned by multiquadric radial basis function (RBF) in space derivatives and by the second order backward differentiation formula in time derivatives. In the chosen equations having analytical solution, dependence of shape parameter to the problem parameters and the number of grid points is taken into account. Then, the shape parameters in an interval are performed in different combination of independent parameters, and the shape parameter associated with the smallest relative error is saved with independent parameters. By means of the data obtained by this way, shape parameter as a function of independent variables is modeled by neural networks. This model enables one to determine the shape parameter without performing any numerical control repeatedly in the considered problem. This approach is firstly proposed for finding an appropriate shape parameter in a specific important physical problem.