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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.