Real-time flood prediction in urban areas is an important tool for city emergency planning. Earlier studies suggest two approaches to predict flooding: a supervised machine learning approach based on observed data and a modeling approach for urban environments based on hydraulics. However, the first approach can only be applied in areas where there is sufficient data on flooding and is not accurate enough for prediction. The second approach can provide accurate predictions even for cities that have never experienced flooding, but models of complex urban environments are not suitable for real-time prediction owing to significant computational complexity. Therefore, we propose a third approach, machine learning supervised by a program. This approach consists of training a lightweight neural network using an integrated flood analysis program composed of multiple hydrologically based models. We demonstrate that this trained neural network is 19.8 times faster and and has accuracy comparable to that of the previous modeling approaches.