利用深度學習演算法預測分段常數函數的反散射問題

Abstract

在本篇論文中，我們對確定非均質介質中的分段常數係數感興趣，這些係數來自於具有聲軟障礙的聲波散射，並已知障礙物的位置及其邊界條件。主要的想法是利用深度神經網絡（DNN），使用深層的全連接層和激活函數，將這些隱藏層疊加起來以模擬和學習數據的非線性特徵或更複雜的行為。我們首先使用前導向散射問題來計算，給予不同的非均勻介質係數推導出不同的總場，進而推出遠場模式。數據集由遠場模式和相應的非均質介質的分段常數係數組成。通過將數據分為訓練集、驗證集和測試集，我們進行監督學習來訓練模型。通過這個模型，我們可以從任何散射場的遠場模式中獲得非均質介質的分段常數係數。

In this thesis, we are interested in determining the piecewise constant coefficients of an inhomogeneous medium from acoustic wave scattering with sound-soft obstacles, given the positions of the obstacles and their boundary conditions. The main idea is to use a deep neural network (DNN), employing deep fully connected layers and activation functions, to stack these hidden layers in order to simulate and learn the nonlinear features or more complex behaviors of the data. We first use the forward scattering problem to calculate different total fields by varying the coefficients of the inhomogeneous medium, and deduce the far-field pattern. The dataset consists of the far-field patterns and the corresponding piecewise constant coefficients of the inhomogeneous medium. By dividing the data into training, validation, and testing sets, we conduct supervised learning to train the model. Through this model, we can obtain the piecewise constant coefficients of the inhomogeneous medium from any far-field pattern of the scattering field.