Abstract: Aiming at the problem of  the position and shape of inverse obstacles with  phaseless far-field data, we proposed  a two-layer gated recurrent unit (GRU) neural network to gated recurrent unit neural network (MGNN) method, and gave the convergence analysis of the proposed  method. Firstly, using the phaseless far-field data and the obstacle boundary curve equation parameters as input and output, through GRU neural network control gate idea and long-term memory function, the network states were selectively updated and the  data characteristics were saved. Secondly, we applied the gradient descent algorithm to update the weights and bias of the model, and  solved the difficulty of  the position and shape of inverse obstacles with phaseless far-field data. Finally,  the effectiveness of the proposed  method was demonstrated by numerical experiments.

Key words: inverse scattering problem, phaseless data, gated recurrent unit (GRU) neural network, convergence