Calculation of Layered Medium Green’s Function Based on Machine Learning Methods

The layered medium is an important model in electromagnetic scattering. In integral equations, the layered medium Green’s function (LMGF) is defined as the fields or potentials generated by an arbitrarily polarized point source in the background of layered medium. The concrete forms of LMGF are different owing to different mathematical definitions or integral equations. However, no matter what specific form is adopted, LMGF is always composed of Sommerfeld integrals. The integrand of these integrals is usually highly oscillatory and slowly attenuating, which leads to a slow convergence when numerical quadrature is utilized. This may greatly slowdown the method of moments (MoM) solution of an integral equation since LMGF has to be repeatedly calculated. A method to accelerate the calculation of LMGF is urgently needed. Nowadays, the research and application of machine learning is increasingly attractive. In this presentation, we propose a machine learning algorithm to accelerate the calculation of LMGF, which is actually a function regression problem in supervised learning. An artificial neural network (ANN) model is constructed based upon a previously proposed matrix-friendly formulation of LMGF. The method utilizes the powerful function estimation ability of ANN to approximate the Green’s function by sophisticated neural network structures. To verify the effectiveness of the proposed method, the LMGF calculated by neural network is compared with the results obtained by direct Sommerfeld integrals. Because LMGF is complex-valued, the real part and imaginary part are trained independently. Additionally, this paper introduces a mind evolutionary algorithm (MEA) to optimize the thresholds and weights of the back propagation neural network (BPNN) to enhance the generalization capability and improve the accuracy of LMGF fitting. Compared with traditional methods, the computational efficiency of LMGF are improved by using the machine learning methods.