Compact and affordable microfluidic pumping is critical for point-of-care applications. Here we proposed a data driven dynamical system to build up a pressure-driven microfluidic pump with a small budget. Firstly, a precision flow sensor is required to obtain the dynamic flow rates as the responses to the driven pressures. Then the flow rate dataset under varying operation pressures is used for data training and model-based system identification. With a first-order or second-order transfer function model, the specifications of pressure-driven microfluidic pumping system are analyzed by the model-based system identification algorithm. Also, all the specifications including the gain, time constant, natural frequency, and damping ratio are updated online as new test data are introduced from more experimental trials. To perform a non-bulky design purpose, the data training system identification is taken on a commercial smartphone. Once the training performance is satisfied, the pressure-driven system could be operated without any flow sensors. The system is used for two-phase flow controls as a demonstration, showing a rapid response of pumping. Dynamic characteristics and the effects of flow resistance on the pumping performance are analyzed to verify its suitability for a wide range of microfluidic applications.