Introducing prior physical and mechanical information to activation functions in artificial neural networks will help them generalize well and overcome some challenges in the present physics-informed machine learning. Inspired by this, the physics-informed kernel function neural networks (PIKFNNs) was proposed for various forward and inverse, linear and nonlinear partial differential equations (PDE) [1]. In the proposed PIKFNNs, a shallow neural network is employed, with physics-informed kernel functions (PIKFs) serving as customized activation functions. The PIKFs fully or partially contain PDE information, which can be chosen as fundamental solutions, Green’s functions, T-complete functions, harmonic functions, radial Trefftz functions, probability density functions, and even the solutions of some linear simplified PDEs, among others. The main difference between the PINNs and the proposed PIKFNNs is that the PINNs add PDE constraints to the loss function, and the proposed PIKFNNs embed PDE information into the activation functions of the neural network. The feasibility and accuracy of the proposed PIKFNNs are validated by some forward and inverse PDE Problems.