  Forecasting time series with extreme events has been a challenging and
prevalent research topic, especially when the time series data are affected by
complicated uncertain factors, such as is the case in hydrologic prediction.
Diverse traditional and deep learning models have been applied to discover the
nonlinear relationships and recognize the complex patterns in these types of
data. However, existing methods usually ignore the negative influence of
imbalanced data, or severe events, on model training. Moreover, methods are
usually evaluated on a small number of generally well-behaved time series,
which does not show their ability to generalize. To tackle these issues, we
propose a novel probability-enhanced neural network model, called NEC+, which
concurrently learns extreme and normal prediction functions and a way to choose
among them via selective back propagation. We evaluate the proposed model on
the difficult 3-day ahead hourly water level prediction task applied to 9
reservoirs in California. Experimental results demonstrate that the proposed
model significantly outperforms state-of-the-art baselines and exhibits
superior generalization ability on data with diverse distributions.
