Eventos Anais de eventos
COBEM 2021
26th International Congress of Mechanical Engineering
ANN-based Mesh-free Method to Solve Partial Differential Equations
Submission Author:
Filipi Teixeira Kunz , SC
Co-Authors:
Filipi Teixeira Kunz, Ney Rafael Secco
Presenter: Filipi Teixeira Kunz
doi://10.26678/ABCM.COBEM2021.COB2021-0094
Abstract
There are well established methods to numerically solve partial differential equations (PDEs), such as Finite Difference, Finite Elements, and Finite Volumes approaches, which usually require the discretization of domain in meshes. However, the generation of high-quality meshes for complex domains is a time-consuming task that demands skilled specialists. In this manuscript we present a mesh-free approach to solve PDEs using feedforward artificial neural networks (ANNs). This methodology involves a training procedure that adjusts ANNs outputs and their derivatives to match PDEs and their associated boundary conditions at a given set of points. We test the procedure by solving canonical PDEs problems of linear advection, steady and unsteady heat transfer, Burgers’ equation, and potential flow. We modify training and network parameters such as optimizer and number of neurons to analyze the outcomes in solution speed and accuracy. This method shows versatility, as the same numerical solver works with hyperbolic, elliptical, and parabolic PDEs. Even though the application of ANN-based solution is computationally more expensive than traditional mesh-based approaches, substantial time can be saved in terms of mesh generation.
Keywords
artificial neural network, Partial differential equation, mesh-free methods
