PINN and KANN approaches for shell structures: sampling strategies and experimental analysis

Abstract

This study compared standard Physics-Informed Neural Networks (PINNs) and Kolmogorov–Arnold Networks (KANs) for thin-shell problems approaching the Kirchhoff–Love limit. With t=0.01, PINNs (3×50 neurons) achieved faster, more stable convergence and lower L² errors than KANs (3×5 neurons), despite having more parameters and halving training time. KANs’ slower convergence and higher final errors indicate limited representational capacity in the current setup. Sampling affected results: Hammersley points yielded slightly better accuracy, particularly for PINNs. Overall, PINNs proved more robust and computationally efficient, while KANs, though promising for compact parametrization, need refinement.