  The computational prediction of wave propagation in dam-break floods is a
long-standing problem in hydrodynamics and hydrology. Until now, conventional
numerical models based on Saint-Venant equations are the dominant approaches.
Here we show that a machine learning model that is well-trained on a minimal
amount of data, can help predict the long-term dynamic behavior of a
one-dimensional dam-break flood with satisfactory accuracy. For this purpose,
we solve the Saint-Venant equations for a one-dimensional dam-break flood
scenario using the Lax-Wendroff numerical scheme and train the reservoir
computing echo state network (RC-ESN) with the dataset by the simulation
results consisting of time-sequence flow depths. We demonstrate a good
prediction ability of the RC-ESN model, which ahead predicts wave propagation
behavior 286 time-steps in the dam-break flood with a root mean square error
(RMSE) smaller than 0.01, outperforming the conventional long short-term memory
(LSTM) model which reaches a comparable RMSE of only 81 time-steps ahead. To
show the performance of the RC-ESN model, we also provide a sensitivity
analysis of the prediction accuracy concerning the key parameters including
training set size, reservoir size, and spectral radius. Results indicate that
the RC-ESN are less dependent on the training set size, a medium reservoir size
K=1200~2600 is sufficient. We confirm that the spectral radius \r{ho} shows a
complex influence on the prediction accuracy and suggest a smaller spectral
radius \r{ho} currently. By changing the initial flow depth of the dam break,
we also obtained the conclusion that the prediction horizon of RC-ESN is larger
than that of LSTM.
