LS-SVM-based nonlinear multi-physical steady-state field coupled problems computing method

Abstract

Multi-physical steady-state field coupled problems are addressed using mesh-based methods, including finite element and finite volume methods, along with their enhancements. To streamline computational complexity, this paper employs a least squares support vector machine (LS-SVM) for tackling the multi-physical steady-state field coupled problems. First, LS-SVM lowers computational complexity by eliminating mesh dependency. Second, it effectively solves multi-physical steady-state field coupled problems with high adaptability. Finally, it can restrain the complex boundary conditions. This paper validates the approach with two case studies: a one-dimensional nonlinear electro-mechanical coupled problem and a two-dimensional nonlinear thermoelectric coupled problem. The LS-SVM method achieved calculation accuracy comparable to the finite element method while offering greater precision and faster computation than both the radial basis function (RBF) interpolation and physics-informed neural network (PINN) methods.