Two-dimensional hydrodynamic models numerically solve full Shallow Water Equations (SWEs). Despite their high accuracy, these models have long simulation run times and therefore are of limited use for exploratory or real-time flood predictions. We investigated the possibility of improving flood modelling speed using Machine Learning (ML). We propose a new method that replaces the computationally expensive parts of the hydrodynamic models with simple and efficient data-driven approximations. Our hypothesis is that by integrating ML with physics-based numerical methods, we can achieve improved generalization performance: that is, the trained model for one case study can be used in other studies without the need for new training. We tested two ML approaches: for the first, we integrated curve fitting, and, for the second, artificial neural networks (ANN) with a finite volume scheme to solve the local inertial approximation of the SWEs. The data-driven models approximated the Momentum Equation, which explicitly solved the time derivative of flow rates. Water depths were then updated by applying a water balance equation. We also tested two different training datasets: the simulated dataset, generated from the results of hydrodynamic model, and the random dataset, generated by directly solving the momentum equation on randomly sampled input data. Various combinations of input features, for example, water slope and depth, were explored. The proposed models were trained in a small hypothetical case and tested in a different hypothetical and in two real case studies. Results showed that the curve-fitting method can be implemented successfully, given sufficient training and input data. The ANN model trained with a random dataset was substantially more accurate than that of the model trained with the simulated dataset. However, it was not successful in the real case studies. The curve-fitting method resulted in better generalization performance and increased the simulation speed of the local inertial model by 23%. Future research should test the performance of ML in terms of an increase in stable time step size and approximation of the full SWEs.