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| 研究生： |
黃帥儒 Huang, Shuai-Ru |
|---|---|
| 論文名稱： |
基於神經網路的逆散射問題方法 A Neural Network Method for the Inverse Scattering Problem |
| 指導教授： | 邱普照 |
| 口試委員: |
邱普照
郭岳承 邱普運 |
| 學位類別： |
碩士
Master |
| 系所名稱： |
理學院 - 應用數學系 Department of Mathematical Sciences |
| 論文出版年： | 2026 |
| 畢業學年度： | 114 |
| 語文別： | 英文 |
| 論文頁數： | 36 |
| 中文關鍵詞： | 聲學逆散射 、神經網路 、前饋式神經網路 、遠場資料 、散射勢 |
| 外文關鍵詞： | acoustic inverse scattering, neural networks, feedforward neural network, farfield data, scattering potential |
| 相關次數： | 點閱：42 下載：1 |
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本論文主要探討以神經網路方法解決聲學逆散射問題之可行性。研究中，我們將散射勢 q(x) 以低維度分區方式加以表示，並透過數值模擬生成遠場資料作為神經網路之輸入。所採用之模型為全連接前饋式神經網路，經由訓練學習遠場資料與散射勢之間的對應關係。數值實驗結果顯示，神經網路能有效捕捉散射勢的主要結構；然而，對於訓練資料分佈之外的幾何形狀，其重建精度仍有限。若欲進一步提升預測準確度，需對問題本身與其數學結構有更深入的理解，並對模型與程式進行適當調整。整體而言，本研究結果顯示神經網路在快速近似解方面具有潛力，但仍需結合嚴謹的反演理論以確保結果之可靠性。
This thesis investigates the feasibility of using neural network methods to solve acoustic inverse scattering problems. The scattering potential q(x) is represented using a low-dimensional partitioned parameterization, and far-field data generated from numerical simulations are used as inputs to the neural network. A fully connected feedforward architecture is employed to learn the mapping between the far-field data and the scattering potential. Numerical results show that the network can effectively capture the main structure of the potential. However, its reconstruction accuracy is limited for geometries outside the training distribution. To further improve prediction accuracy, a deeper understanding of the underlying problem and its mathematical structure is required, along with appropriate refinements of the model and implementation. Overall, the results demonstrate that neural networks have strong potential as fast approximation tools, but they should be combined with rigorous inversion theory to ensure reliability.
Contents
1 Introduction 1
2 Methodology 3
2.1 Input layer 3
2.2 Hidden Layers . 3
2.3 Output Layer 4
3 Parameter Setting and Training 5
3.1 Approximation of the Forward Map 5
3.2 Supervised Learning Setting and Network Architecture 7
4 Results 8
4.1 Selection of Hidden Layer Architecture 8
4.2 Reconstruction Results for the 2 × 2 Configuration 9
4.3 Extension to the 3 × 3 Configuration 10
5 Discussion 13
5.1 Effect of Discretization Resolution 13
5.2 Underfitting and Overfitting Considerations 14
6 Conclusion 16
A Background on Acoustic Scattering 17
B Numerical Implementation 20
B.1 Far-field Data Computation 20
B.2 Training Data Generation (2 × 2) 23
B.3 Prediction for Benchmark Configurations (2 × 2) 25
B.4 Prediction for an Out-of-Distribution Geometry (2 × 2) 28
B.5 Training Data Generation (3 × 3) 30
B.6 Prediction for Benchmark Configurations (3 × 3) 32
Bibliography 36
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