AI RESEARCH
Scaling Laws and Pathologies of Single-Layer PINNs: Network Width and PDE Nonlinearity
arXiv CS.LG
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ArXi:2603.12556v1 Announce Type: new We establish empirical scaling laws for Single-Layer Physics-Informed Neural Networks on canonical nonlinear PDEs. We identify a dual optimization failure: (i) a baseline pathology, where the solution error fails to decrease with network width, even at fixed nonlinearity, falling short of theoretical approximation bounds, and (ii) a compounding pathology, where this failure is exacerbated by nonlinearity.