A Neural Network for Recovering the Dirichlet Eigenvalues with the Far-field Data
This paper is concerned with an inverse eigenvalue problem of the obstacles with the Dirichlet boundary conditon in the sound field. We develop a data-driven neural network. First ,we establish the mathematical models for the internal eigenvalue problem and the external scattering problem of the obstacles with Dirichlet boundary conditions. Then,we con-struct a multi-layer feedforward neural network with sequence to sequence structure. The key ingredient of the network is to use backpropagation error and self-learning to update the hyperparameters. Finally,under the premise of unknown scatterer information,the Dirichlet eigenvalues of the obstacles are reconstructed using the far-field data. Numerical experiments show the effectiveness of this method.
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