AKAPINN: Adaptive Kolmogorov-Arnold Physics-Informed Neural Networks for Approximating Solutions to Quasilinear Partial Differential Equations

This paper presents a controlled comparative study of adaptive Kolmogorov-Arnold Physics-Informed Neural Networks (KAN-PINN) for solving nonlinear strain-limiting partial differential equations in solid mechanics. The approach employs a mesh-free methodology with an exact hard boundary ansatz, a robust pseudo-Huber residual loss function, and a multi-stage Adam-to-L-BFGS optimizer schedule. Three training runs across varying material-parameter pairs are evaluated to assess the method's effectiveness for structural mechanics problems involving material nonlinearity.