Deep Learning Based Multiple Obstacles Inverse Scattering Problem

The study of multiple obstacles inverse scattering problem has a wide range of practical applications,such as in the field of ocean exploration,to detect the location and size of deep-sea fish swarm;In the field of automobile autonomous driving,the driving path is planned according to the obstacles in front of the car.However,due to the strong discomfort of multiple obstacles inverse scattering and the low efficiency of traditional numerical methods in big data processing,it is difficult to use traditional numerical methods in practical application to retrieve the geometric information of obstacle position energy based on measured data.Deep learning has great advantages in big data processing and is often used to process complex structures and large-sample high-dimensional data.Therefore,this paper considers using deep learning method to solve multiple obstacles inverse scattering problem.In the acoustic field of two-dimensional space,where a homogeneous medium has multiple impenetrable obstacles with known boundary conditions and all of which are acoustic soft boundary conditions,the problem of multiple obstacles scattering is presented when the incident wave is plane wave.First of all,based on potential theory and jump relations,integral equations of the scattering problem of multiple obstacles are derived.Based on the Fredholm theorem,the uniqueness of the solution for the scattering problem of multiple obstacles is proved.Nystr(?)m method is used to solve the scattering problem of multiple obstacles,which comes to the far field mode of the scattering field.This problem is also worked out with two examples,of which one is the single-shape obstacle of two circles,and the other is the hybrid-shape obstacle of a kite-like shape and a circle.Then,based on attention mechanism,double layer neural network model of inversion multiple obstacles position parameter is structured.The far field mode of the scattering field is used as input,and the multiple obstacles position parameters are used as output,using the attention mechanism to obtain the eigenvalues of the far field model,the relative error as the loss function of the model,and the gradient descent method to update model of weights and bias,then the position parameters of the multiple obstacles was inverted.Finally,taking two circular single-shape obstacles,and a hybrid shape(a kite-loke shape and a circle)obstacle as examples,the number of observation points,the amount of data,the number of waves and the observation aperture as variables respectively,the far field mode of the scattering field and the constructed neural network model are used to invert the position of obstacles.The experimental results show that the multiple obstacles position inversion model constructed in this paper can effectively invert the position of multiple obstacles.