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研究生: 白佩鑫
Pai, Pei-Hsin
論文名稱: 粒子調適之無網格神經粒子法應用於流體動態模擬
A Neural Particle Method with Adaptive Particle Refinement for Hydrodynamic Modeling
指導教授: 戴義欽
Tai, Yih-Chin
學位類別: 碩士
Master
系所名稱: 工學院 - 水利及海洋工程學系
Department of Hydraulic & Ocean Engineering
論文出版年: 2023
畢業學年度: 112
語文別: 中文
論文頁數: 134
中文關鍵詞: 物理導向類神經網絡無網格神經粒子法界面追蹤技術粒子調適技術機器學習
外文關鍵詞: Physics-­informed neural networks, Neural particle method, Interface­tracking, Adaptive particle, Machine learning
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  • 摘要 i 英文延伸摘要 ii 誌謝 xi 目錄 xii 圖片 xiv 表格 xvi 第一章 緒論 1 1.1 研究動機與目的 1 1.2 文獻回顧 2 1.2.1 傳統數值方法對於移動邊界的處理 2 1.2.2 從資料導向到物理導向的機器學習 5 1.2.3 Lagrange 框架下的 PINNs 6 1.3 研究方法 8 1.4 本文架構 8 第二章 模型理論與方法 9 2.1 控制方程式 9 2.1.1 Navier­Stokes 方程式 9 2.1.2 Eulerian/Lagrangian 的轉換 10 2.2 粒子重置方法 11 2.2.1 粒子調適技術 (Adaptive particle refinement) 11 2.2.2 界面追蹤技術 (Interface tracking) 13 2.2.3 緩衝帶界面融合技術 (Buffer zone interface merging) 13 2.3 物理導向的機器學習 17 2.3.1 機器學習原理 17 2.3.2 物理導向的神經網絡 (PINNs) 22 2.4 無網格神經粒子法 26 2.4.1 模型輸入和輸出 26 2.4.2 粒子加速度與推估速度 26 2.4.3 損失函數 (Loss function) 27 2.4.4 NPM­LA 的推理過程 (Inference) 27 2.4.5 位置更新 (Update position) 28 2.4.6 時間推演 (Time marching) 28 2.5 Approximation distance functions (ADF) 30 2.6 模型與超參數設定 31 第三章 數值特性探討 35 3.1 平板流 (Poiseuille flow) 35 3.2 旋轉方形流體 (Rotating square fluid patch) 48 第四章 應用案例 69 4.1 模擬設置說明 69 4.2 乾床潰壩實驗 (Dam break on the dry bed) 73 4.3 濕床潰壩實驗 (Dam break on the wet bed) 77 第五章 計算效率探討 87 5.1 超參數與模型架構測試 87 5.1.1 學習率 89 5.1.2 激活函數 89 5.1.3 神經網絡大小 90 5.2 高階變數微分效率測試 95 5.3 遷移式學習 (Transfer learning) 101 第六章 結論及建議 111 6.1 總結 111 6.2 未來方向及建議 113 參考文獻 115

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