Curvature-based importance density functions enable dynamic grid adaptation in KANs, cutting relative errors by 25.3% on synthetic functions, 9.4% on Feynman data, and 23.3% on Helmholtz PDEs versus input-density baselines.
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations,
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A Dynamic Framework for Grid Adaptation in Kolmogorov-Arnold Networks
Curvature-based importance density functions enable dynamic grid adaptation in KANs, cutting relative errors by 25.3% on synthetic functions, 9.4% on Feynman data, and 23.3% on Helmholtz PDEs versus input-density baselines.