Surrogate Model for Shallow Water Equations Solvers with Deep Learning

Abstract: Shallow water equations are the foundation of most models for flooding and river hydraulics analysis. These physics-based models are usually expensive and slow to run, thus not suitable for real-time prediction or parameter inversion. An attractive alternative is surrogate model. This work introduces an efficient, accurate, and flexible surrogate model, NN-p2p, based on deep learning and it can make point-to-point predictions on unstructured or irregular meshes. The new method was evaluated and compared against existing methods based on convolutional neural networks (CNNs), which can only make image-to-image predictions on structured or regular meshes. In NN-p2p, the input includes both spatial coordinates and boundary features that can describe the geometry of hydraulic structures, such as bridge piers. All surrogate models perform well in predicting flow around different types of piers in the training domain. However, only NN-p2p works well when spatial extrapolation is performed. The limitations of CNN-based methods are rooted in their raster-image nature which cannot capture boundary geometry and flow features exactly, which are of paramount importance to fluid dynamics. NN-p2p also has good performance in predicting flow around piers unseen by the neural network. The NN-p2p model also respects conservation laws more strictly. The application of the proposed surrogate model was demonstrated by calculating the drag coefficient $C_D$ for piers and a new linear relationship between $C_D$ and the logarithmic transformation of pier's length/width ratio was discovered.