Kolmogorov-Arnold Networks for Free-Boundary Partial Differential Equations

arXiv:2610.02084v1 Announce Type: cross Abstract: We study free-boundary problems within a physics-informed framework using Kolmogorov-Arnold network (KAN) approximations. The proposed approach incorporates obstacle constraints, partial differential equation (PDE) inequalities, complementarity conditions, and boundary conditions through residual-based loss functions. We consider a linear elliptic obstacle problem, a nonlinear p-Laplacian obstacle problem, and a time-dependent one-phase Stefan problem. The proposed KAN solver is compared with physics-informed neural network (PINN) and residual-network baselines. Numerical experiments show that KANs achieve low relative L^2 and L^infty errors while accurately resolving contact regions and moving interfaces. The results indicate that KAN representations provide an effective alternative for solving free-boundary PDEs.

Source: arXiv cs.LG | 2026-10-02