AKAPINN: Adaptive Kolmogorov-Arnold Physics-Informed Neural Networks for approximating solutions to quasilinear partial differential equations

This paper introduces AKAPINN (Adaptive Kolmogorov-Arnold Physics-Informed Neural Networks), a mesh-free approach that combines Kolmogorov-Arnold networks with physics-informed learning for solving nonlinear strain-limiting partial differential equations. The method incorporates an exact hard boundary ansatz, a robust pseudo-Huber residual loss function, and a multi-stage training strategy transitioning from Adam to L-BFGS optimizer. Three distinct training runs across varying material-parameter pairs are evaluated within a controlled comparative study framework.