As the important power interfaces connecting renewable energy and power grid, inverters are widely used in the novel power systems. It is urgent to establish the dynamic models of grid-tied inverters to analyze the transient behavior of grid-tied system before actual grid connection. In order to make up for the defects that physical mechanism modeling methods and conventional data-driven modeling methods for power electronic converters (PECs), this paper integrates differential algebraic equations (DAEs) into neural networks, i.e. formulating the differential algebraic neural networks (DANNs), to capture the high-dimensional nonlinear dynamic characteristics of grid-tied inverters. By comparing the transient behavior of grid-tied inverters based on actual simulation devices and dynamic models based on DANNs, it is proved that the proposed modeling method can capture the dynamic characteristics of grid-tied inverters with considerable accuracy and generalization under different grid-tied conditions and external interferences.