Author

Haopeng Quan

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Aug 2026

Spectral analysis of hard-constraint PINNs: The spatial modulation mechanism of boundary functions.

Physics-Informed Neural Networks with hard constraints (HC-PINNs) enforce boundary conditions exactly via a trial function ansatz u˜=A+B·N, yet the theoretical mechanisms governing their training dynamics have remained unexplored. This work establishes a Neural Tangent Kernel (NTK) framework for HC-PINNs, revealing tha...

Yuchen Xie, Honghang Chi, Haopeng Quan et al. · Neural Networks · 0 citations