In recent decades, anomalous and nonergodic dynamics are topical issues in almost all disciplines. In 2004, the phrase “anomalous is normal” was used in a title of a PRL paper, which reveals that the diffusion of classical particles on a solid surface has rich anomalous behavior controlled by the friction coefficient, meaning that anomalous dynamics phenomena are ubiquitous in the natural world. This talk first introduces the dynamics from a physical and atomistic way, by considering the random walk of the diffusing particles, then derives the partial differential equations with integral-differential operators governing the PDFs of the various statistical observables. Finally, we discuss the (traditional and deep learning based) numerical methods for the newly build PDEs.