analiza aiqbench
This research demonstrates the efficacy of Kolmogorov-Arnold Networks (KANs) as a robust alternative to Physics-Informed Neural Networks (PINNs) for solving complex free-boundary partial differential equations. By incorporating obstacle constraints and moving interfaces through residual-based loss functions, KANs achieve superior accuracy in resolving contact regions compared to standard baselines. The study validates KANs as a promising architecture for advancing physics-informed machine learning in mathematical modeling.
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.
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.
Numerical Analysis (math.NA); Machine Learning (cs.LG)
arXiv:2610.02084 [math.NA]
(or arXiv:2610.02084v1 [math.NA] for this version)
https://doi.org/10.48550/arXiv.2610.02084 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Text integral sub licența deschisă a publicației · 196 cuvinte
Subiecte conexe
IGA-KAN: Isogeometric Analysis with Physics-Informed Closed-Form Kolmogorov-Arnold Networks for Forward and Inverse PDEs
arXiv · 6 oct. 2026
Tackling Failure Modes of PINNs and PIKANs Using Conflict-Free Gradients
arXiv · 15 sept. 2026
PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs
arXiv · 23 iul. 2026
Reliability-Aware Hard--Soft Physics-Informed Neural Networks for Robust Learning of Challenging Partial Differential Equations
arXiv · 23 iul. 2026