Kolmogorov-Arnold Networks for Free-Boundary Partial Differential Equations
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 regio...
| Authors | Tan Phuong Dong Le |
|---|---|
| Primary category | math.NA |
| Published | 1 October 2026 |
| Last updated at source | 1 October 2026 |
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