Surrogate Model for Shallow Water Equations Solvers with Deep Learning
- URL: http://arxiv.org/abs/2112.10889v1
- Date: Mon, 20 Dec 2021 22:30:11 GMT
- Title: Surrogate Model for Shallow Water Equations Solvers with Deep Learning
- Authors: Yalan Song, Chaopeng Shen, Xiaofeng Liu
- Abstract summary: This work introduces an efficient, accurate, and flexible surrogate model, NN-p2p, based on deep learning.
The input includes both spatial coordinates and boundary features that can describe the geometry of hydraulic structures.
NN-p2p has good performance in predicting flow around piers unseen by the neural network.
- Score: 6.123836425156534
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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.
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