# Kolmogorov-Arnold Networks for Free-Boundary Partial Differential Equations

arXiv: https://arxiv.org/abs/2610.02084 · HTML: https://mlsanity.com/paper/2610.02084/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 23 references that are in the map.
- First posted on arXiv 1 Oct 2026.

## Builds on (most cited first, 4 of 4)

- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Deep learning of free boundary and Stefan problems](https://mlsanity.com/paper/2006.05311/) (2020)

## Abstract (arXiv)

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 L2 and L^∞ errors while accurately resolving contact regions and moving interfaces. The results indicate that KAN representations provide an effective alternative for solving free-boundary PDEs.