Reproduce “Neural Tangent Kernel Analysis to Probe Convergence in Physics-informed Neural Solvers: PIKANs vs. PINNs” on OpenResearch
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About this paper
Salah A. Faroughi, Farinaz Mostajeran
The paper extends neural tangent kernel analysis to Chebyshev-based physics-informed Kolmogorov–Arnold networks, modeling how training affects solution values and PDE residuals. It examines temporal subdivision for a damped, periodically driven beam over ten seconds, passing each window’s prediction to the next. With eight windows, cPIKAN’s relative L2 error was 7.06 × 10⁻³ versus PINN’s 7.79 × 10⁻¹ in this experiment.
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