In the context of high penetration of renewables and power electronics, the need to build dynamic models of power system components based on accessible measurement data has become urgent. To address this challenge, firstly, a neural ordinary differential equations (ODE) module and a neural differential-algebraic equations (DAE) module are proposed to form a data-driven modeling framework that accurately captures components' dynamic characteristics and flexibly adapts to various interface settings. Secondly, analytical models and data-driven models learned by the neural ODE and DAE modules are integrated together and simulated simultaneously using unified transient stability simulation methods. Finally, the neural ODE and DAE modules are implemented with Python and made public on GitHub. Three simple but representative cases of excitation controller modeling, classical synchronous machine modeling, and equivalent load modeling of a regional power network are carried out in the IEEE-39 system and 2383wp system. Neural dynamic model-integrated simulations are compared with the original model-based ones to verify the feasibility and potentiality of the proposed neural ODE and DAE modules.