研究生: |
徐捷耀 Syu, Jie-Yao |
---|---|
論文名稱: |
透過計算和深度學習探索非局部奇異擾動微分方程的解 Exploring the Solution of Singular Differential Equation with Non-local Boundary Conditions by Calculating and Deep Learning |
指導教授: |
李俊璋
Lee, Chiun-Chang 陳人豪 Chen, Jen-Hao |
口試委員: |
林得勝
Lin, Te-Sheng 吳昌鴻 Wu, Chang-Hong |
學位類別: |
碩士 Master |
系所名稱: |
理學院 - 計算與建模科學研究所 Institute of Computational and Modeling Science |
論文出版年: | 2023 |
畢業學年度: | 111 |
語文別: | 英文 |
論文頁數: | 51 |
中文關鍵詞: | 非局部微分方程 、奇點 、深度學習 |
外文關鍵詞: | non-local differential equation, singularity, deep learning |
相關次數: | 點閱:70 下載:0 |
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In this thesis, we address the issue of boundary influence by interior points in the context of the non-local singularly perturbed equation. On the other hand, we provide an example with exact solutions and employ neural networks to analyze its solutions. Moreover, we identify several potential challenges that may arise. In the first section, we explore computational approaches to estimate the behavior of the solution and its derivatives. In the second section, we investigate the problems that may occur when using neural networks to handle such equations, along with their underlying causes.
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