Machine-Learning-Based Hybrid Method for the Multilevel Fast Multipole Algorithm

In this letter, a hybrid translation computation method for the multilevel fast multipole algorithm (MLFMA) is proposed based on machine learning. The hybrid method combines both generalized regression neural network (GRNN) and artificial neural network (ANN) to replace the traditional translation procedure during the solving process of the MLFMA. Based on the data corresponding to every one of the interaction list boxes at each level, the hybrid neural network is trained. Comparing with the previous machine learning method in this field, the proposed model is more general, and with lower complexity since it inherits the accuracy of the GRNN as well as the efficiency of the ANN. To the best of our knowledge, it is for the first time that the ANN is integrated into the MLFMA. Numerical examples are benchmarked to illustrate the reliability and capability, thus making it possible to solve similar problems during the fast inhomogeneous plane wave algorithm solving process in the multilayered medium.