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Shallow water equations are the foundation of most models for flooding andriver hydraulics analysis. These physics-based models are usually expensive andslow to run, thus not suitable for real-time prediction or parameter inversion.An attractive alternative is surrogate model. This work introduces anefficient, accurate, and flexible surrogate model, NN-p2p, based on deeplearning and it can make point-to-point predictions on unstructured orirregular meshes. The new method was evaluated and compared against existingmethods based on convolutional neural networks (CNNs), which can only makeimage-to-image predictions on structured or regular meshes. In NN-p2p, theinput includes both spatial coordinates and boundary features that can describethe geometry of hydraulic structures, such as bridge piers. All surrogatemodels perform well in predicting flow around different types of piers in thetraining domain. However, only NN-p2p works well when spatial extrapolation isperformed. The limitations of CNN-based methods are rooted in theirraster-image nature which cannot capture boundary geometry and flow featuresexactly, which are of paramount importance to fluid dynamics. NN-p2p also hasgood performance in predicting flow around piers unseen by the neural network.The NN-p2p model also respects conservation laws more strictly. The applicationof the proposed surrogate model was demonstrated by calculating the dragcoefficient $C_D$ for piers and a new linear relationship between $C_D$ and thelogarithmic transformation of pier's length/width ratio was discovered.

Surrogate Model for Shallow Water Equations Solvers with Deep Learning