This paper is concerned with the application of a machine learning approach to inverse elastic scattering problems via neural networks. In the forward problem, the displacements are approximated by linear combinations of the fundamental tensors of the Cauchy-Navier equations of elasticity, which are expressed in terms of sources placed inside the elastic solid. From the near-field measurement data, a two-layer neural network method consisting of a gated recurrent unit to gate recurrent unit has been used to reconstruct the shape of an unknown elastic body. Moreover, the convergence of the method is proved. Finally, the feasibility and effectiveness of the presented method are examined through numerical examples.

In this paper, a boundary integral equation method is proposed for the fluid-solid interaction scattering problem, and a high-precision numerical method is developed. More specifically, by introducing the Helmholtz decomposition, the corresponding problem is transformed into a coupled boundary value problem for the Helmholtz equation. Based on the integral equation method, the coupled value problem is reduced to a system of three coupled hypersingular integral equations. Semi-discrete and fully-discrete collocation methods are proposed for the singular integral equations. The presented method is based on trigonometric interpolation and discretized singular operators applied to differentiated interpolation. The convergence of the method is verified by a numerical experiment.