本研究旨在發展一套結合物理資訊類神經網路（Physics-Informed Neural Networks, PINNs）與神經粒子方法（Neural Particle Method, NPM）之數值模擬方法，以應對工程領域中常見的大變形（finite deformation）問題。此類問題廣泛存在於土木、地質與材料工程中，具高度非線性與複雜邊界行為，雖然傳統方法如有限元素法（Finite Element Method, FEM）能夠處理此類問題，但在大變形情況下，常面臨計算不穩定、邊界處理困難及對大量資料依賴等限制。
PINNs 將物理問題的數學模型與深度神經網絡結合，形成具備物理約束的深度神經網絡，專門用於求解偏微分方程（Partial Differential Equations, PDEs）問題。通過在神經網絡訓練過程中整合物理定律，即使在數據稀缺的條件下依然能進行高效且精確的預測。本研究應用 PINNs 於靜態固體力學問題，涵蓋彈性體與塑性材料模擬，其中塑性行為包含理想彈塑性模型與德魯克-普拉格模型（Drucker–Prager model）。此外，在動態大變形模擬方面，分別使用 PINNs 與 NPM 方法，模擬固體之運動行為，或模擬利用 $mu(I)$ 流變學理論之顆粒流體。研究由彈性體與塑性體的簡化模型出發，逐步擴展至邊坡滑動（slope sliding）等應用場景進行模擬與驗證。
本研究系統性探討了各類大變形物理模型的精度與穩定性，並以多個二維問題作為測試案例，與傳統數值方法（如有限元素法）進行比較。結果顯示，PINNs 與 NPM 在求解固體力學與顆粒流動問題方面，能達到與傳統數值方法相當的準確度與穩定性，特別是在資料不足的情況下展現其優勢與潛力。本研究證實了 PINNs 與 NPM 在大變形問題中的可行性與有效性，未來可望作為一種新興的數值工具，應用於地工災害預警、材料行為模擬與結構安全分析等工程領域。

This study aims to develop a numerical simulation framework that integrates Physics-Informed Neural Networks (PINNs) and the Neural Particle Method (NPM) to address finite deformation problems commonly encountered in engineering. These problems are prevalent in civil, geotechnical, and materials engineering, characterized by strong nonlinearity and complex boundary behavior. Although traditional methods such as the Finite Element Method (FEM) are capable of handling such problems, they often face challenges under large deformation conditions, including numerical instability, difficulty in boundary handling, and a heavy reliance on extensive data.
PINNs combine the mathematical models of physical problems with deep neural networks, forming physics-constrained learning architectures specifically designed for solving partial differential equations (PDEs). By incorporating physical laws into the training process, PINNs can achieve accurate and efficient predictions even under data-scarce conditions. This study applies PINNs to static solid mechanics problems, including the simulation of elastic and plastic materials. The plasticity component includes both ideal elastoplastic models and the Drucker–Prager model. For dynamic large deformation problems, both PINNs and NPM are employed—PINNs for simulating solid body motion, and NPM for modeling granular flows based on the μ(I) rheology framework. The study begins with simplified models of elastic and plastic materials and gradually extends to practical applications such as slope sliding, to validate and demonstrate the proposed methods.
This study systematically investigates the accuracy and stability of various physical models under finite deformation, using multiple two-dimensional benchmark problems and comparing them against traditional numerical methods such as FEM. The results show that PINNs and NPM can achieve comparable accuracy and stability in solving both solid mechanics and granular flow problems. Their advantage becomes particularly evident in scenarios with limited data. This research confirms the feasibility and effectiveness of PINNs and NPM in handling large deformation problems, and suggests their potential as emerging numerical tools for applications in geotechnical hazard prediction, material behavior modeling, and structural safety assessment.

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