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Small-scale liquid flows on solid surfaces provide convincing details in liquid animation, but they are difficult to be simulated with efficiency and fidelity, mostly due to the complex nature of the surface tension at the contact front where liquid, air, and solid meet. In this paper, we propose to simulate the dynamics of new liquid drops from captured real-world liquid flow data, using deep neural networks. To achieve this goal, we develop a data capture system that acquires liquid flow patterns from hundreds of real-world water drops. We then convert raw data into compact data for training neural networks, in which liquid drops are represented by their contact fronts in a Lagrangian form. Using the LSTM units based on recurrent neural networks, our neural networks serve three purposes in our simulator: predicting the contour of a contact front, predicting the color field gradient of a contact front, and finally predicting whether a contact front is going to break or not. Using these predictions, our simulator recovers the overall shape of a liquid drop at every time step, and handles merging and splitting events by simple operations. The experiment shows that our trained neural networks are able to perform predictions well. The whole simulator is robust, convenient to use, and capable of generating realistic small-scale liquid effects in animation.