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PINN
PDE and Machine Learning (1): Physics-Informed Neural Networks
From finite differences to PINNs: automatic differentiation, PDE residual losses, NTK-based training pathologies, Burgers inverse problems, and a side-by-side comparison with FEM and neural operators. Seven figures …
Ordinary Differential Equations (18): Frontiers and Series Finale
The series finale. Survey four research frontiers reshaping how we model dynamics -- Neural ODEs, delay equations, stochastic differential equations, and fractional calculus -- then take stock of the entire 18-chapter …