Deterministic models of complex flows are challenging and computationally expensive. We propose here, for the first time, a computationally efficient data-driven Lagrangian stochastic approach to predict liquid flow inside a mechanically agitated vessel. The model relies on the input of a short driver data set to predict the full flow field. We investigate the capability of zeroth, first and second order models over a wide range of flow conditions including different impeller configurations and rotational speeds. The first and second order models provide good predictions of local flow properties, with the first order model being slightly superior. The technique is also capable of predicting flow well outside the range of experimental conditions.