Fast and reliable prediction of riverine flow velocities is important in many applications, including flood risk management. The shallow water equations (SWEs) are commonly used for prediction of the flow velocities. However, accurate and fast prediction with standard SWE solvers is challenging in many cases. Traditional approaches are computationally expensive and require high-resolution riverbed profile measurement ( bathymetry) for accurate predictions. As a result, they are a poor fit in situations where they need to be evaluated repetitively due, for example, to varying boundary condition (BC), or when the bathymetry is not known with certainty. In this work, we propose a two-stage process that tackles these issues. First, using the principal component geostatistical approach (PCGA) we estimate the probability density function of the bathymetry from flow velocity measurements, and then we use multiple machine learning algorithms to obtain a fast solver of the SWEs, given augmented realizations from the posterior bathymetry distribution and the prescribed range of BCs. The first step allows us to predict flow velocities without direct measurement of the bathymetry. Furthermore, the augmentation of the distribution in the second stage allows incorporation of the additional bathymetry information into the flow velocity prediction for improved accuracy and generalization, even if the bathymetry changes over time. Here, we use three solvers, referred to as PCA-DNN (principal component analysis-deep neural network), SE (supervised encoder), and SVE (supervised variational encoder), and validate them on a reach of the Savannah river near Augusta, GA. Our results show that the fast solvers are capable of predicting flow velocities with good accuracy, at a computational cost that is significantly lower than the cost of solving the full boundary value problem with traditional methods.

翻译：对河水流速度的快速和可靠预测在许多应用中非常重要,包括洪水风险管理。浅水方程(SWES)通常用于预测水流速度。然而,在许多情况中,与标准SWE解析器的准确和快速预测具有挑战性。传统方法在计算上成本高昂,需要高分辨率河床剖面测量(测深)来准确预测。因此,在需要反复评估的情况中,它们不合适,例如,由于边界状况不同(BC),或水深测量尚不确定。在这项工作中,我们提出一个处理这些问题的两阶段进程。首先,我们利用主要组成部分的地理-水分流精确度预测(PCGA),我们从流动速度测量中估算测深水的概率密度,然后我们利用多机算算算算来获得SWES快速解析器的快速解析器。由于从后方位测深测深线分布和公分数的定值范围(BCSBS),第一个步骤让我们预测水深的流流,而无需直接测量SEAR 准确性精确度分析,然后在水路流流中进行水路流流流数据分析。SBILILLILA, 数据流中, 数据流的流数据流数据流数据流数据流的精确分析,我们又显示,我们测测算法的精确度分析,我们测测算法的精度数据流的精度数据流的精度数据流的精度数据流的精度数据流的精度数据流的精度数据流的精确度将显示,我们的精确度数据流的精确度数据流的精确度,我们的精确度数据流数据流数据, 。