Machine learning and reduced order computation of a friction stir welding model

Abstract

The friction stir welding process can be modeled using a system of heat transfer and Navier-Stokes equations with a shear dependent viscosity. Finding numerical solutions of this system of nonlinear partial differential equations over a set of parameter space, however, is extremely time-consuming. Therefore, it is desirable to find a computationally efficient method that can be used to obtain an approximation of the solution with acceptable accuracy. In this paper, we present a reduced basis method for solving the parametrized coupled system of heat and Navier-Stokes equations using a proper orthogonal decomposition (POD). In addition, we apply a machine learning algorithm based on an artificial neural network (ANN) to learn (approximately) the relationship between relevant parameters and the POD coefficients. Our computational experiments demonstrate that substantial speed-up can be achieved while maintaining sufficient accuracy.