MMN-4965
LS-SVR for the fractional fourth-order partial differential equations
Marziyeh Felahat;Abstract
Fractional fourth-order partial differential equations find various applications such as image denoising, electrostatics, and geometric modeling. In this paper, we propose a new supervised machine learning algorithm for such problems. To do so, we develop a simulation method based on least squares support vector regression (LS-SVR). A polynomial kernel is used to approximate the solution in the training process by considering an inverse viewpoint to the residual function. For minimizing the loss function, we use the Petrov-Galerkin method for the constraints in the proposed LS-SVR. We study the stability and convergence of the method by providing some numerical examples and by illustrating the error behavior as the degree of the solution increases.
Vol. 26 (2025), No. 2, pp. 767-783