A neural-FEM approach for the effective permeability estimation of a composite magnetic shielding mortar

A mixed Neural-Finite Element Method (FEM) strategy is proposed for the evaluation of magnetic permeability for the equivalent homogenized material of a magnetic shielding mortar containing ferromagnetic particles. The approach is based on a two phases procedure: in the first phase thousands of FEM meshes representing the same sample geometry, with different inclusions distribution, are used to compute the magnetic field; the data so achieved are then used to fed a feedforward neural network, which is able to extract the relationship, among the quantity of magnetic material used (input), its magnetic permeability (input) and the equivalent material characteristic (output). These two phases are unsupervised as in a machine learning approach in such a way that the estimation can be refined automatically. The obtained results are validated by comparison with experimental data available from literature.