Neural-Network Solution of the Nonuniqueness Problem in Acoustic Scattering Using Wavelets

Abstract

The solution of Helmholtz integral equation for acoustic scattering is confronted with a nonuniquness issue at the characteristic wave numbers. In this paper, a neural network-based solution to this problem is proposed. To start with, the moment matrix resulting from the discretized Helmholtz integral equation is sparsified using appropriate wavelet techniques. This sparse matrix is, further, analyzed to obtain unique patterns that characterize its structure. As a result, a proper training set of these patterns is constructed and utilized to train a back propagation neural network. The trained network is capable of predicting the scattered acoustic field for the wave numbers at which the problem doesn't suffer any nonuniqueness. Moreover, the network can also be used to obtain the scattered field even for such wavenumbers at which the nonuniqueness occurs. Comparing the neural network outputs with the exact solutions demonstrates the validity and efficiency of the proposed method.

Keywords:

• Aacoustic Scattering
• Helmholtz Integral Equation
• Neural Networks
• Daubechies Wavelet Family
• Nonuniqueness
• Characteristic Wavenumber