研究生: |
陳姿君 Chen, Tzu-Chun |
---|---|
論文名稱: |
利用無網格神經粒子法初探流固耦合問題 Preliminary Investigation of Fluid-Structure Interaction Using a Neural Particle Method |
指導教授: |
林冠中
Lin, Kuan-Chung |
學位類別: |
碩士 Master |
系所名稱: |
工學院 - 土木工程學系 Department of Civil Engineering |
論文出版年: | 2025 |
畢業學年度: | 113 |
語文別: | 中文 |
論文頁數: | 82 |
中文關鍵詞: | 深度學習 、PINNs 、NPM 、流體 、固體 、流固耦合 、有限元素法 |
外文關鍵詞: | Deep learning, Physics-informed Neural Networks (PINNs), Neural Particle Method (NPM), Fluid, Solid, Fluid-structure interaction (FSI), Finite Element Method (FEM) |
相關次數: | 點閱:12 下載:0 |
分享至: |
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
深度學習作為一種先進的人工智慧技術,已在各工程領域展現巨大的應用潛力。物理資訊神經網路(Physics‐informed Neural Networks, PINNs)將已知的物理定律直接融入神經網路的訓練過程中,使其在沒有大量標註數據的情況下,也能夠學習並預測複雜物理系統的行為,本研究使用的無網格神經粒子法(Neural Particle Method, NPM)是一種基於拉格朗日的物理資訊神經網路(PINNs)數值方法。本研究旨在探索深度學習於流固耦合問題之應用,透過無網格神經粒子法(NPM),模擬流體與彈性體之間的相互作用。本研究選取三種典型流場案例:純水流、固定擋板與凸起障礙物,以及固體於動態與靜態載重下之變形。透過無網格神經粒子法(NPM)進行模擬,並與傳統有限元素法(Finite Element Method, FEM)之結果進行比較,結果顯示,NPM 模擬所得的數值分佈與 FEM 結果高度一致,證實了本方法之準確性與數值穩定性。最後,本研究初步探討了無網格神經粒子法(NPM)於動態流固耦合問題之應用,並對流體與固體之間的相互作用進行了初步的分析,其變形型態相似,雖因邊界處理策略不同,局部銜接區仍見形貌差異,但整體變形型態一致。目前結果為深度學習於流固耦合問題之應用提供了一個初步的探索,並為相關領域提供了一個新的研究方向。
Deep learning, an advanced artificial intelligence technology, has shown remarkable potential across engineering disciplines. Physics informed neural networks (PINNs) embed known physical laws directly into the training process, allowing complex physical systems to be learned and predicted without large labeled datasets. The numerical scheme adopted here—the Neural Particle Method (NPM)—is a Lagrangian-based PINN numerical method. This study explores the use of deep learning for fluid–structure interaction (FSI) by applying NPM to simulate the interplay between fluids and elastic solids. Three representative cases are examined: (i) pure water flow, (ii) flow past a fixed baffle and a protruding obstacle, and (iii) deformation of a solid under dynamic and static loads. NPM results are compared with those from the conventional Finite Element Method (FEM); the two sets of solutions exhibit excellent agreement, confirming the accuracy and numerical stability of NPM. A preliminary application of NPM to dynamic FSI is also presented. Although differences in boundary treatment strategies lead to minor local discrepancies at the interface, the overall deformation patterns remain consistent. These findings provide an initial demonstration of a meshfree, data efficient deep learning approach to FSI analysis and point to promising future research directions.
[1] Henning Wessels, Christian Weißenfels, and Peter Wriggers. The neural particle method–an updated Lagrangian physics-informed neural network for computational fluid dynamics. Computer Methods in Applied Mechanics and Engineering, 368:113127, 2020.
[2] Warren S. McCulloch and Walter Pitts. A logical calculus of the ideas immanent in nervous activity. The Bulletin of Mathematical Biophysics, 5:115–133, 1943.
[3] Frank Rosenblatt. The perceptron: a probabilistic model for information storage and organization in the brain. Psychological Review, 65(6):386, 1958.
[4] Kurt Hornik, Maxwell Stinchcombe, and Halbert White. Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks. Neural Networks, 3(5):551–560, 1990.
[5] Isaac Elias Lagaris, Aristidis Likas, and Dimitrios I. Fotiadis. Artificial neural networks for solving ordinary and partial differential equations. IEEE Transactions on Neural Networks, 9(5):987–1000, 1998.
[6] Maziar Raissi, Paris Perdikaris, and George E. Karniadakis. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378:686–707, 2019.
[7] Ehsan Haghighat, Maziar Raissi, Adrian Moure, Hector Gomez, and Ruben Juanes. A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics. Computer Methods in Applied Mechanics and Engineering, 379:113741, 2021.
[8] Diab W. Abueidda, Qiyue Lu, and Seid Koric. Meshless physics-informed deep learning method for three-dimensional solid mechanics. International Journal for Numerical Methods in Engineering, 122(23):7182–7201, 2021.
[9] Sijun Niu, Enrui Zhang, Yuri Bazilevs, and Vikas Srivastava. Modeling finite-strain plasticity using physics-informed neural network and assessment of the network performance. Journal of the Mechanics and Physics of Solids, 172:105177, 2023.
[10] Zikun Luo, Lei Wang, and Mengkai Lu. A stepwise physics-informed neural network for solving large deformation problems of hypoelastic materials. International Journal for Numerical Methods in Engineering, 124(20):4453–4472, 2023.
[11] Francisco Sahli Costabal, Simone Pezzuto, and Paris Perdikaris. δ-PINNs: Physics-informed neural networks on complex geometries. Engineering Applications of Artificial Intelligence, 127:107324, 2024.
[12] Chengping Rao, Hao Sun, and Yang Liu. Physics-informed deep learning for computational elastodynamics without labeled data. Journal of Engineering Mechanics, 147(8):04021043, 2021.
[13] Enrui Zhang, Ming Dao, George Em Karniadakis, and Subra Suresh. Analyses of internal structures and defects in materials using physics-informed neural networks. Science Advances, 8(7):eabk0644, 2022.
[14] Luning Sun, Han Gao, Shaowu Pan, and Jian-Xun Wang. Surrogate modeling for fluid flows based on physics-constrained deep learning without simulation data. Computer Methods in Applied Mechanics and Engineering, 361:112732, 2020.
[15] Xiaowei Jin, Shengze Cai, Hui Li, and George Em Karniadakis. NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations. Journal of Computational Physics, 426:109951, 2021.
[16] Jinshuai Bai, Ying Zhou, Yuwei Ma, Hyogu Jeong, Haifei Zhan, Charith Rathnayaka, Emilie Sauret, and Yuantong Gu. A general neural particle method for hydrodynamics modeling. Computer Methods in Applied Mechanics and Engineering, 393:114740, 2022.
[17] Pei Hsin Pai, Heng Chuan Kan, Hock Kiet Wong, and Yih Chin Tai. A neural particle method with interface tracking and adaptive particle refinement for free surface flows. Communications in Computational Physics, 36(4):1021–1052, 2024.
[18] Mayank Raj, Pramod Kumbhar, and Ratna Kumar Annabattula. Physics-informed neural networks for solving thermo-mechanics problems of functionally graded material. arXiv preprint arXiv:2111.10751, 2021.
[19] Gaétan Raynaud. Study of physics-informed neural networks to solve fluid-structure problems for turbine-like phenomena. Ecole Polytechnique, Montreal (Canada), 2021.
[20] Hesheng Tang, Yangyang Liao, Hu Yang, and Liyu Xie. A transfer learning-physics-informed neural network (TL-PINN) for vortex-induced vibration. Ocean Engineering, 266:113101, 2022.
[21] Xiantao Fan and Jian-Xun Wang. Differentiable hybrid neural modeling for fluid-structure interaction. Journal of Computational Physics, 496:112584, 2024.
[22] Ping Zhu, Zhonglin Liu, Ziqing Xu, and Junxue Lv. An adaptive weight physics-informed neural network for vortex-induced vibration problems. Buildings, 15(9):1533, 2025.
[23] Kurt Hornik, Maxwell Stinchcombe, and Halbert White. Multilayer feedforward networks are universal approximators. Neural Networks, 2(5):359–366, 1989.
[24] David E. Rumelhart, Geoffrey E. Hinton, and Ronald J. Williams. Learning representations by back-propagating errors. Nature, 323(6088):533–536, 1986.
[25] Diederik P. Kingma. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980, 2014.
[26] Dong C. Liu and Jorge Nocedal. On the limited memory BFGS method for large scale optimization. Mathematical Programming, 45(1):503–528, 1989.
[27] Arieh Iserles. A First Course in the Numerical Analysis of Differential Equations. Number 44. Cambridge University Press, 2009.
[28] E. Hairer, G. Wanner, and O. Solving. II: Stiff and Differential-Algebraic Problems. Springer, 1991.
[29] John Charles Butcher. A history of Runge-Kutta methods. Applied Numerical Mathematics, 20(3):247–260, 1996.
[30] Jens Berg and Kaj Nyström. A unified deep artificial neural network approach to partial differential equations in complex geometries. Neurocomputing, 317:28–41, 2018.
[31] Peter Wriggers. Nonlinear Finite Element Methods. Springer Science & Business Media, 2008.
[32] Stefan Elfwing, Eiji Uchibe, and Kenji Doya. Sigmoid-weighted linear units for neural network function approximation in reinforcement learning. Neural Networks, 107:3–11, 2018.
[33] Facundo Del Pin and Iñaki Çaldichoury. LS-DYNA® 980: Recent developments, application areas and validation process of the incompressible fluid solver (ICFD) in LS-DYNA. In 13th International LS-DYNA Users Conference, 2016.
[34] Facundo Del Pin and Iñaki Çaldichoury. LS-DYNA c R7: Strong fluid-structure interaction (FSI) capabilities and associated meshing tools for the incompressible CFD solver (ICFD), applications and examples. In 9th European LS-DYNA Conference, 2013.