In reality many networks, such as information storage networks, can be modelled as a multi-state stochastic flow network. The reliability of an information storage network is the probability that the network is able to deliver the required amount of information data to the specified server, and its an important metric to assess the performance of an information storage network. Most existing multi-state network reliability assessment algorithms are calculated using very small capacity vectors. However, calculating the reliability of such a network requires reuse of algorithms and is inefficient when the network size, demand, etc., changes rapidly, resulting in managers not making timely decisions accordingly. In order to obtain reliability metrics quickly, this paper proposes a dynamic network reliability prediction model based on deep neural networks (DNNs), which allows the corresponding reliability to be obtained quickly even when the network is changing rapidly. Finally, a local information storage network is used as an example for validation to illustrate the feasibility of the prediction model.