A multilayer perceptron neural model for the differentiation of Laplacian 3-D finite-element solutions

An MLP neural model is presented in order to evaluate accurately derivatives of rough finite-element numerical solutions to three-dimensional Laplacian electromagnetic problems. The adopted neural approach overcomes the limitations inherent to advanced postprocessing techniques based on Poisson integrals because it is applicable to domains of arbitrary shape. The training of the neural network is performed off-line by employing a modular class of harmonic polynomial functions. Accuracy can be predetermined at the user's convenience by suitably selecting the order of the polynomial functions in the off-line training. The tests performed show that accurate results are achieved with a negligible online computational effort. A further advantage of this neural model is its easy implementation in existing postprocessing modules.