This study presents a novel approach to improving the accuracy of flood forecast models with limited training data. Flood forecast information is crucial for early evacuation planning. However, the probability of flooding caused by continuous heavy rainfall is increasing, even in areas where we have not installed flood forecasts. New methods exist to provide flood forecasts, but they require long-term observations and regular updating of extensive data on the basin. Existing methods of providing new flood forecast information require long-term observations and regular updates of extensive data on the watershed. These requirements are related to the construction time and cost of providing flood forecasts. To address this issue, we propose Informed Neural Networks (INN) that integrate existing domain knowledge of river engineering to enhance the performance of flood forecasts with a limited amount of training data. We evaluated the performance of our proposed method with Japanese real-world river water levels and compared it to conventional methods such as artificial neural networks (ANN). Our results demonstrate that the INN can significantly improve forecasting accuracy with only a small amount of training data, comparable to conventional methods trained with eight times the amount of flood data. This study highlights the potential of INN as a novel approach for accurate and efficient flood forecasting with limited training data.