人工智慧材料搜尋與優化

課程大綱

第1週：PINN基礎與科學計算典範，涵蓋PDE數值法與正反向問題概念 第2週：PINN建模與Poisson方程式，學習軟/硬式約束及邊界條件 第3週：配置點法、高斯積分、弱式理論與能量型PINN基礎 第4週：能量型PINN進階、Neumann混合邊界與神經網路函數表示 第5週：PINN扭轉力學、三角網格數值積分與多種子解的驗證 第6週：不規則幾何域、橢圓與多邊形PINN及材料微結構應用 第7週：一般多邊形域、可學習邊界函數神經網路與多孔材料界面 第8週：PINN暫態熱傳基礎、時空取樣與基本熱參數反演 第9週：暫態熱傳混合邊界、異質非等向性傳導與熱性質反演 第10週：長時間熱傳預測、複雜孔洞處理與PINN收斂性分析 第11週：PINN波動方程式、二階時間微分 第12週：硬式約束、殘差自適應取樣、脈衝波激振 第13週：PINN特徵值問題、聲子、力學模態與材料能帶結構 第14週：PINN反問題、高維與非線性多物理場及材料數位孿生 Week 1: PINN basics, PDE numerical methods, and forward/inverse problems Week 2: PINN modeling, Poisson equation, Dirichlet/Neumann boundaries & constraints Week 3: Collocation methods, Gaussian quadrature, weak form, and energy PINNs Week 4: Energy PINNs, Neumann boundaries, and neural network representations Week 5: PINN torsion mechanics, triangular meshes, and solution verification Week 6: Irregular domains, polygonal PINNs, and material microstructures Week 7: Polygonal domains, learnable boundary neural networks, and interfaces Week 8: Transient heat transfer, space-time sampling, and thermal inversion Week 9: Mixed boundaries, heterogeneous conduction, and inverse thermal properties Week 10: Long-term heat transfer, complex pores, and PINN convergence analysis Week 11: PINN wave equation, wave energy Week 12: Hard constraints, adaptive sampling, pulse forces Week 13: PINN eigenproblems, phonons, mechanical modes, and band structures Week 14: PINN inverse problems, nonlinear multiphysics, and differentiable digital twins