  AI for partial differential equations (PDEs) has garnered significant
attention, particularly with the emergence of Physics-informed neural networks
(PINNs). The recent advent of Kolmogorov-Arnold Network (KAN) indicates that
there is potential to revisit and enhance the previously MLP-based PINNs.
Compared to MLPs, KANs offer interpretability and require fewer parameters.
PDEs can be described in various forms, such as strong form, energy form, and
inverse form. While mathematically equivalent, these forms are not
computationally equivalent, making the exploration of different PDE
formulations significant in computational physics. Thus, we propose different
PDE forms based on KAN instead of MLP, termed Kolmogorov-Arnold-Informed Neural
Network (KINN) for solving forward and inverse problems. We systematically
compare MLP and KAN in various numerical examples of PDEs, including
multi-scale, singularity, stress concentration, nonlinear hyperelasticity,
heterogeneous, and complex geometry problems. Our results demonstrate that KINN
significantly outperforms MLP regarding accuracy and convergence speed for
numerous PDEs in computational solid mechanics, except for the complex geometry
problem. This highlights KINN's potential for more efficient and accurate PDE
solutions in AI for PDEs.
