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Smart materials structures with multifield coupling properties have been widely used in the latter years. Some methodologies have been developed to study fracture problems in piezoelectric and magnetoelectroelastic (MEE) materials using the boundary element method (BEM). However, relatively limited attention has been paid to inverse problems. Identification problems are usually ill-conditioned, which implies that gradient search methods might not have a good performance, whilst Newton-based search methods are computationally expensive. Additionally, the presence of noise in the measured data affects the convergence of these methods. In this paper, we study the application of neural networks to damage identification of multifield materials, in particular to MEE materials. A particular training set division has been applied to improve the identification results, even for high noise levels. A hypersingular BEM is used to obtain the solution of the direct problem (elastic displacements and magnetic and electric potentials) and create the training set. [ABSTRACT FROM AUTHOR]