A Surrogate Model for Shallow Water Equations Solvers with Deep Learning
Publication: Journal of Hydraulic Engineering
Volume 149, Issue 11
Abstract
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.
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Data Availability Statement
All model source code, case setup, and result data generated or used during the study are available in a repository hosted on GitHub (https://github.com/psu-efd/Surrogate_Modeling_SWEs). The source code for pyHMT2D can be found on GitHub at (https://github.com/psu-efd/pyHMT2D).
Acknowledgments
This work is supported by a seed grant from the Institute of Computational and Data Sciences at the Pennsylvania State University.
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Information & Authors
Information
Published In
Journal of Hydraulic Engineering
Volume 149 • Issue 11 • November 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Dec 28, 2021
Accepted: Jun 13, 2023
Published online: Sep 5, 2023
Published in print: Nov 1, 2023
Discussion open until: Feb 5, 2024
ASCE Technical Topics:
- Artificial intelligence and machine learning
- Computer programming
- Computing in civil engineering
- Design (by type)
- Drag (fluid dynamics)
- Engineering fundamentals
- Flow (fluid dynamics)
- Fluid dynamics
- Fluid flow
- Fluid mechanics
- Geometrics
- Highway and road design
- Hydraulic models
- Hydrologic engineering
- Models (by type)
- Neural networks
- Shallow water
- Simulation models
- Water (by type)
- Water and water resources
- Water management
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