A Surrogate Model for Shallow Water Equations Solvers with Deep Learning

Physics-based models (PBMs), such as shallow water equations (SWEs) solvers, have been widely used in flood simulation and river hydraulics analysis. However, they are usually computationally expensive and unsuitable for parameter optimizations that need many runs. An alternative is the machine learning (ML) method, which can be used to construct computationally efficient surrogates for PBMs that can approximate their input-output dynamics. Among many ML techniques, convolutional neural network (CNN) is a prevalent method for image-to-image regressions on structured or regular meshes (e.g., mapping from the boundary conditions to flow solutions of SWEs). However, CNN-based methods have significant limitations because of their raster-image nature. Such methods cannot precisely capture the boundary geometry of obstacles and near-field flow features, which are of paramount importance to fluid dynamics. We introduced an efficient, accurate, and flexible neural network (NN) surrogate model [which is based on deep learning and can make point-to-point (p2p) predictions on unstructured meshes] called NN-p2p. The new method was evaluated and compared against CNN-based methods. NN-p2p improves the accuracy of the near-field flow prediction with a mean relative error of 0.56% for the velocity magnitude around piers with unseen length/width ratios. It also respects conservation laws more strictly than the CNN-based models and performs reasonably well for spatial extrapolation. The surrogate reduces computing time by almost 3-orders of magnitude in comparison with its corresponding PBM. Moreover, as a demonstration of the NN-p2p model's practical applicability, we calculated drag coefficient using NN-p2p for piers of varying length-to-width ratios and obtained a novel linear relationship between the drag coefficient and the logarithmic transformation of the pier's geometry.