A Machine Learning Approach to Optimize Quadrature Rule for Isogeometric Analysis

Isogeometric analysis (IGA) is a numerical method to solve partial differential equations, which takes the computer-aided design (CAD) model for the analysis of various field variables. Gaussian quadrature rule is generally employed as a numerical integration scheme to compute the quantities, such as stiffness matrix, force vector, for an elemental patch in IGA. With the increase in Gauss quadrature points, the accuracy of the numerical integration increases. However, it increases the computational cost as well. In this work, a machine learning (ML) technique, artificial neural network (ANN), is employed to get the required Gauss quadrature points for a non-uniform rational B-spline (NURBS) geometry. The developed classification model successfully estimates the required Gauss quadrature points for a given patch of geometry.