Multi-frequency Machine Learning Algorithm For Acoustic Inverse Source Problem

The inverse source problem is to identify or recover the source information from the measured scattered waves.It is an important inverse scattering problem.It has been widely used in various science and engineering applications.Due to the superiority of machine learning algorithm in solving inverse problem,this paper proposes a machine learning algorithm to solve inverse source problem based on a fully understanding of the classic iterative algorithm.We consider the inverse source problem in the homogeneous background medium and use multi-frequency detected data.The deep neural network takes the scattering data as input,and the reduced mean error is adopted as the loss function to optimize the parameters of the neural network.Eventually,the neural network will recover the source function in the region.The main advantage of the algorithm is that the neural network approximates the source function,without too many constraint assumptions,and the calculation is relatively simple.Numerical examples are used to verify the feasibility of the proposed algorithm.At the same time,by adding random noise to the experimental data,we find that the proposed machine learning algorithm has good stability.