Automated two-dimensional field computation in nonlinear magnetic media using Hopfield neural networks

It is well known that the computation of magnetic fields in nonlinear magnetic media may be carried out using different approaches. In the case of problems involving complex geometries and/or magnetic media, numerical techniques become especially more appealing. In this paper, we present an automated integral equation approach using which two-dimensional field computations may be carried out in nonlinear magnetic media. This approach is constructed in terms of a continuous Hopfield neural network (HNN) whose neuron activation functions are set to mimic the vectorial magnetic properties of the media. Using well-established HNN energy minimization algorithms, an automated solution of the problem is then obtained. The approach has been implemented and resulted in good agreement with finite-element (FE) computations. Details of the approach, computations, and FE results are given in this paper.