Physics-informed multi-stage surrogate model for urban flooding

doi:10.3785/j.issn.1008-973X.2026.07.017

Journal of ZheJiang University (Engineering Science)

2026, Vol. 60

Issue (7): 1557-1566 DOI: 10.3785/j.issn.1008-973X.2026.07.017

Physics-informed multi-stage surrogate model for urban flooding

Ting SU1(

),Yueping XU1,*(

),Quanjun WANG2,Hua ZHONG3,Jianqun JIANG1

1. College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
2. Faculty of Engineering and Information Technology, University of Melbourne, Melbourne 3052, Australia
3. Nanjing Hydraulic Research Institute, Nanjing 210029, China

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Abstract

A multi-stage surrogate model named LSTM-LFM-SRU was developed to address the high computational cost and limited real-time capability of traditional hydrodynamic models. The urban flood process was divided into two stages: one-dimensional drainage through pipe networks and two-dimensional surface inundation. Long short-term memory (LSTM) networks and a combination of a low-fidelity physical model (LFM) with a super-resolution U-shaped convolutional neural network (SRU) were adopted to replace the corresponding stages. A flood prediction framework was constructed by combining data-driven methods with physical information. The multi-stage surrogate model was applied to a case study in the Xiasha area of Hangzhou. A 20-hour intense rainfall-induced inundation event was simulated within 5.31, with its computational efficiency reaching 12.7 times that of the high-precision hydrodynamic models. The one-dimensional LSTM-based surrogate achieved an average Nash-Sutcliffe Efficiency value of 0.94, while the two-dimensional LFM-SRU model reduced the Root Mean Square Error by 17.2% compared with the LFM-U-net model.

Key words： urban flooding multi stage surrogate model long short-term memory(LSTM) low-fidelity physical model (LFM) super-resolution U-shaped convolutional neural network (SRU)

Received: 17 April 2025 Published: 23 May 2026

CLC:

TP 183

Fund: 国家自然科学基金资助项目（52309038）；浙江省重点研发计划资助项目（2021C03017）.

Corresponding Authors: Yueping XU E-mail: 22312105@zju.edu.cn;yuepingxu@zju.edu.cn

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Cite this article:

Ting SU,Yueping XU,Quanjun WANG,Hua ZHONG,Jianqun JIANG. Physics-informed multi-stage surrogate model for urban flooding. Journal of ZheJiang University (Engineering Science), 2026, 60(7): 1557-1566.

URL:

https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2026.07.017 OR https://www.zjujournals.com/eng/Y2026/V60/I7/1557

基于物理信息的城市洪涝多阶段替代模型

针对传统水力学模型计算量大且难以满足实时预测需求的问题，研发融合长短期记忆网络（LSTM）、低精度物理模型（LFM）与基于超分辨率技术的U形卷积神经网络（SRU）的多阶段替代模型LSTM-LFM-SRU. 模型将洪涝过程划分为一维管网排水与二维地表淹没2个阶段，分别采用LSTM与LFM-SRU进行替代建模，构建数据驱动与物理信息融合的内涝预测框架. 在杭州下沙的应用结果表明，本研究中所构建的多阶段替代模型能在5.31 s内完成一场20 h强降雨引发的城市淹没过程模拟，计算效率提升至高精度的水动力学模型的12.7倍，其中一维替代模型LSTM的平均纳什效率系数达到0.94，二维替代模型LFM-SRU相比于LFM-U-net模型在均方根误差上下降了17.2%.

关键词： 城市洪涝, 多阶段, 替代模型, 长短期记忆网络(LSTM), 低精度物理模型(LFM), 基于超分辨率技术的U形卷积神经网络(SRU)

Fig.1 Overview of study area

Fig.2 Construction process of multi-stage surrogate model for urban flooding

Tab.1 Summary of 6 historical extreme rainfall events at Hangzhou station

Tab.2 Calibrated parameters results of physical process model

Fig.3 Verification results of physical process model

Fig.4 Structure of super-resolution U-shaped convolutional neural network

Tab.3 Static physical characteristics inputted into SRU model

Fig.5 Comparison of overflow results between SWMM simulation and LSTM model prediction

Tab.4 Comparison of simulation performance metrics for 2D surrogate model

Fig.6 Comparison of simulation results of 1D-2D coupled surrogate model

Tab.5 Comparison of performance metrics in comparative experiment

Fig.7 Simulation results of different model groups in comparative experiments

Tab.6 Comparison of computational efficiency among different model combinations


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