Aug 2026
Spectral analysis of hard-constraint PINNs: The spatial modulation mechanism of boundary functions.
This work establishes a Neural Tangent Kernel (NTK) framework for HC-PINNs, revealing that the boundary function B acts as a multiplicative spatial modulator that fundamentally reshapes the kernel eigenspectrum-a mechanism fundamentally distinct from additive penalty terms in soft-constrained formulations.
Yuchen Xie, Honghang Chi, Haopeng Quan et al.
· Neural Networks · 0 citations