A least squares–support vector machine for learning solution to multi-physical transient-state field coupled problems

The least squares–support vector machine (LS-SVM) method has achieved remarkable success in solving electromagnetic equations. However, the boundaries of the entire computational domain for solving multi-physical transient-state field coupled problems are varied. The shape functions used in mesh-based methods (such as the finite element method and the finite volume method) are constructed on meshes, so it is difficult to obtain an accurate solution using mesh-based methods. To overcome this disadvantage of mesh-based methods, the LS-SVM method is presented in this paper for solving multi-physical transient-state field coupled problems. First, the time step of the transient field is iterated by the Crank–Nicolson (C-N) method. Following that, the Karush–Kuhn–Tucker (KKT) optimality conditions are used, and the quadratic programming problem is transformed into the solution of a system of equations. Finally, an immune algorithm is used to determine the shape parameters, and the accuracy of the solution is improved. The efficiency of the LS-SVM method was demonstrated by solving a two-dimensional transient-state electrothermal coupled problem and a two-dimensional transient-state electromagnetic–fluid coupled problem. The method was compared with the finite element method (or finite volume method), and the same order of calculation accuracy was obtained by the LS-SVM method. Compared to the physics-informed neural network, a more accurate solution was obtained and shorter computation times were required by the LS-SVM method.