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.
翻译:在大坝爆发的洪水中,对波浪传播的计算预测是流体动力学和水文学中长期存在的一个问题。到目前为止,基于圣维南方程式的常规数字模型是主导方法。在这里,我们显示一个在最低数据量上训练有素的机器学习模型能够帮助预测一维大坝爆发洪水的长期动态行为,且准确度令人满意。为此,我们使用Lax-Wendroff数字方案解决了单维南方程式的单维南方程式,并将储油层计算回声状态网络(RC-ESN)与模拟结果的数据集结合起来。我们展示了RC-ES-NSN流流流流流深度的良好预测能力。我们先预测了大坝破裂洪水中的波传动行为286个时点,而根正方位错误(RMSE)小于0.01,这比常规的短期内存(LSTM)模型要差81个时程。为了展示了RC-NSS的流中程速度,我们也展示了RES-NS流速度模型的精确度,我们提供了一个精度模型的精度分析。