KANs for solving Burgers' PDEs Code

Abstract

We systematically investigate four Kolmogorov–Arnold Network (KAN) architectures, B-Spline, Chebyshev, Hermite, and Legendre, as physics-informed solvers for the 1D viscous Burgers' equation across two viscosity regimes (ν = 1.0 and ν = 0.005) and two polynomial degrees (k = 3 and k = 5). All KAN variants are benchmarked against a standard Physics-Informed Neural Network (PINN) baseline and a high-resolution Finite Difference (FD) reference solver.