This paper presents a fast JAX-based implementation of grid-dependent Physics-Informed Kolmogorov-Arnold Networks (PIKANs) for solving Partial Differential Equations (PDEs). PIKANs are an alternative to Multilayer Perceptrons (MLPs) in Physics-Informed Neural Networks (PINNs), offering better interpretability and efficiency with fewer parameters. The authors propose an adaptive training scheme for PIKANs, incorporating known MLP-based PINN techniques, an adaptive state transition scheme to avoid loss function peaks between grid updates, and a methodology for designing PIKANs with alternative basis functions. Through comparative experiments, they demonstrate that these adaptive features significantly enhance training efficiency and solution accuracy. The results highlight the effectiveness of PIKANs in improving performance for PDE solutions, making them a superior alternative in scientific and engineering applications. Key contributions include a new computational framework for KANs, an adaptive transition method to address loss function jumps after grid extensions, and a general direction for designing PIKANs with alternative basis functions, emphasizing the importance of preserving grid dependency for more adaptive training.This paper presents a fast JAX-based implementation of grid-dependent Physics-Informed Kolmogorov-Arnold Networks (PIKANs) for solving Partial Differential Equations (PDEs). PIKANs are an alternative to Multilayer Perceptrons (MLPs) in Physics-Informed Neural Networks (PINNs), offering better interpretability and efficiency with fewer parameters. The authors propose an adaptive training scheme for PIKANs, incorporating known MLP-based PINN techniques, an adaptive state transition scheme to avoid loss function peaks between grid updates, and a methodology for designing PIKANs with alternative basis functions. Through comparative experiments, they demonstrate that these adaptive features significantly enhance training efficiency and solution accuracy. The results highlight the effectiveness of PIKANs in improving performance for PDE solutions, making them a superior alternative in scientific and engineering applications. Key contributions include a new computational framework for KANs, an adaptive transition method to address loss function jumps after grid extensions, and a general direction for designing PIKANs with alternative basis functions, emphasizing the importance of preserving grid dependency for more adaptive training.