Eventos Anais de eventos
COBEM 2021
26th International Congress of Mechanical Engineering
Unsupervised Machine Learning technique for solving flows of generalized Newtonian fluids.
Submission Author:
Bernardo Brener , RJ
Co-Authors:
Bernardo Brener, Roney Thompson
Presenter: Bernardo Brener
doi://10.26678/ABCM.COBEM2021.COB2021-0779
Abstract
A physics informed neural networks framework is employed in the present work in order to approximate the solution of partial differential equations through an unsupervised task. More specifically, it is solved here the set of linear and non-linear equations that rules the flows generalized Newtonian fluids. This innovative methodology uses the main advantage of automatic differentiation of neural networks to build a loss function that obeys a set of partial differential equations. When the training algorithm of the network is run, it converges to the solution of the specified equations by minimizing the loss function. The input of the network is the local coordinates of the problem and the output is the solution of the set of equations, which in the following application is the velocity and stress fields. The boundary and initial conditions are satisfied using the more traditional approach of machine learning techniques of a supervised task where a loss function is built using an error metric between the known output and the predicted one. This is added in the methodology simply by summing both loss functions, as the information in the boundary is previously known. This methodology has the advantage of not using any numerical differentiation which naturally does not bring any problems related to numerical methods. Furthermore, this methodology is mesh-independent. It was already successfully applied and validated for solving ordinary and partial differential equations in the literature. It is proposed here to apply this methodology for solving flows of non-Newtonian fluids, namely flows of generalized Newtonian fluids. The solution obtained with the neural networks is compared with the ones obtained through the classical approach of numerical methods and analytical solutions when available. It is shown that this methodology can successfully be applied to resolve this class of problems providing accurate solutions in all cases analyzed.
Keywords
machine learning, Non-Newtonian fluid, Artificial neural networks
