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Offshore wind farm modelling has been an area of rapidly increasing interest over the last two decades, with numerous analytical as well as computational-based approaches developed, in an attempt to produce designs that improve wind farm efficiency in power production. This work presents a Machine Learning (ML) framework for the rapid modelling of wind farm flow fields, using a Deep Neural Network (DNN) neural network architecture, trained here on approximate turbine wake fields, calculated on the state-of-the-art wind farm modelling software FLORIS. The constructed neural model is capable of accurately reproducing single wake deficits at hub-level for a 5MW wind turbine under yaw and a wide range of inlet hub speed and turbulence intensity conditions, at least an order of magnitude faster than the analytical wake-based solution method, yielding results with 1.5% mean absolute error. A superposition algorithm is also developed to construct flow fields over the whole wind farm domain by superimposing individual wakes. A promising advantage of the present approach is that its performance and accuracy are expected to increase even further when trained on high-fidelity CFD or real-world data through transfer learning, while its computational cost remains low.