Deep learning has been an important tool for solving high-dimensional or highly nonlinear PDEs. However, its computational efficiency, e.g., running time and accuracy, is still the bottleneck that might prevent its popularization. In this talk, we introduce two fast algorithms for solving nonlinear and high-dimensional PDEs and eigenvalue problems. One is motivated by the two grid method in traditional nonlinear solvers and another one is motivated by the self-paced learning in machine learning that mimics human cognitive.