Comparison of neural network and polynomial models for the approximation of nonlinear and anisotropic ferromagnetic materials

Nonlinear magnetic problems can be solved efficiently by applying the iterative Newton-Raphson method in a finite-element framework. At the beginning of each nonlinear iteration, the magnetic reluctivity and the differential reluctivity must be determined in every element of the mesh. As a consequence, the time required for building the linear system to be solved, strongly depends on the evaluation time of the applied material models. Moreover, the accuracy and the smoothness of the material models affect the convergence rate of the Newton-Raphson method. Three methods for representing material properties are compared from a computational point of view. The magnetisation curves of nonlinear isotropic ferromagnetic materials are commonly approximated by cubic splines. However, it is observed that polynomials and feedforward neural networks have also been adopted for this purpose. It is shown that these, although having some attractive properties, should not be applied for approximating magnetisation curves. The same holds for more complex relations, such as the anisotropic reluctivity curves of grain-oriented steel. Although feedforward neural networks become more appealing for these types of mappings, they do not offer a computational advantage compared with the bicubic spline representation.