Kernel functions can represent the high-dimensional implicit feature space without computing the coordinates of the data but rather by simply computing the inner products between the images of all pairs of data. Therefore, the kernel-based collocation solvers can be considered as the one of the most promising methods for numerical solutions of high-dimensional PDEs.

Introducing any underlying physical laws as prior information, a group of physics informed kernels could be derived to provide the efficient and accurate numerical solutions of PDEs in the kernel-based collocation solvers. Several numerical examples demonstrate the efficiency and accuracy of the proposed physics informed kernel collocation solver.