Roberto Bentivoglio
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Urbanization and climate change have intensified the need for rapid and accurate predictions of flash floods, especially in urban areas. Although numerical models produce accurate predictions, their computational cost makes them impractical for real-time simulations. Several machine learning models have been proposed as surrogates for such applications. However, most models focus only on predicting water depths and have little insight into the required variety and amount of data to train such models.In this study, we present a Convolutional Neural Network (CNN) surrogate model designed to predict both water depths and flow velocities for urban pluvial flooding, using as inputs a rainfall hyetograph and seven hydro-morphological descriptors, such as aspect, curvature, slope, Manning’s roughness coefficient, topographic wetness index, flow accumulation, and digital terrain model.To train and test our approach, we considered a dataset of numerical simulations carried out using a 2D shallow-water hydrodynamic modeling in the city of Matera, Italy. For the physical-based simulations, we considered several rainfall hyetographs, either obtained from real events or derived from design scenarios for different return periods, and simulated the associated pluvial floods propagation extracting as outputs the corresponding maps of the maximum envelope of the water depths and flow velocities. The CNN model obtained a testing 0.37 cm mean absolute error (MAE), 1.7 cm root mean squared error (RMSE), and 0.80 critical success index (CSI) for water depth predictions, and 0.054 m/s MAE, 0.178 m/s RMSE, and 0.84 CSI for flow velocity predictions. The CNN model was 116.5 times faster than the physically-based hydrodynamic model using the same computational hardware.We also analyzed the effect of different combinations of rainfall events to train and validate the CNN model, showing that it benefits from a balanced dataset in terms of different return periods and presence of both synthetic and real hyetographs. We then employed the model to extrapolate urban flooding for higher return periods (200, 300, 500, and 1000 years), showing that the model can predict well severe extreme events, as highlighted by a high correlation between predicted maximum water volumes and total rainfall.This study contributes to the practical usability of deep learning models by providing essential support for real-time or low lead-time urban flash flood predictions, which are crucial for effective early warning and emergency management.
...
Urbanization and climate change have intensified the need for rapid and accurate predictions of flash floods, especially in urban areas. Although numerical models produce accurate predictions, their computational cost makes them impractical for real-time simulations. Several machine learning models have been proposed as surrogates for such applications. However, most models focus only on predicting water depths and have little insight into the required variety and amount of data to train such models.In this study, we present a Convolutional Neural Network (CNN) surrogate model designed to predict both water depths and flow velocities for urban pluvial flooding, using as inputs a rainfall hyetograph and seven hydro-morphological descriptors, such as aspect, curvature, slope, Manning’s roughness coefficient, topographic wetness index, flow accumulation, and digital terrain model.To train and test our approach, we considered a dataset of numerical simulations carried out using a 2D shallow-water hydrodynamic modeling in the city of Matera, Italy. For the physical-based simulations, we considered several rainfall hyetographs, either obtained from real events or derived from design scenarios for different return periods, and simulated the associated pluvial floods propagation extracting as outputs the corresponding maps of the maximum envelope of the water depths and flow velocities. The CNN model obtained a testing 0.37 cm mean absolute error (MAE), 1.7 cm root mean squared error (RMSE), and 0.80 critical success index (CSI) for water depth predictions, and 0.054 m/s MAE, 0.178 m/s RMSE, and 0.84 CSI for flow velocity predictions. The CNN model was 116.5 times faster than the physically-based hydrodynamic model using the same computational hardware.We also analyzed the effect of different combinations of rainfall events to train and validate the CNN model, showing that it benefits from a balanced dataset in terms of different return periods and presence of both synthetic and real hyetographs. We then employed the model to extrapolate urban flooding for higher return periods (200, 300, 500, and 1000 years), showing that the model can predict well severe extreme events, as highlighted by a high correlation between predicted maximum water volumes and total rainfall.This study contributes to the practical usability of deep learning models by providing essential support for real-time or low lead-time urban flash flood predictions, which are crucial for effective early warning and emergency management.
Journal article
(2026)
-
Roberto Bentivoglio, Sebastiaan Nicolas Jonkman, Elvin Isufi, Riccardo Taormina
Flood hazard maps are essential for protection and emergency plans, yet their probabilistic application is constrained by the computational cost of numerical models. Deep learning surrogates can provide orders of magnitude faster predictions, but their use for uncertainty quantification in realistic settings and their ability to incorporate hydraulic structures remain largely unexplored. Studying deep learning surrogates for probabilistic flood maps is non-trivial because of the lack of reference ground-truth data that might lead to misleading confidence in predictions. Moreover, hydraulic structures are challenging to include due to their generally unidimensional nature. In this work, we investigate the use of deep learning surrogates for realistic, large-scale flood simulations in case studies with hydraulic structures under diverse boundary conditions. To this end, we employ the multi-scale shallow-water-equations graph neural network (mSWE-GNN) that enjoys transferability to different boundary conditions and locations and whose graph-based architecture allows to represent structures such as canals, underpasses, and elevated elements as inputs. To address the lack of reference ground-truth data, we further introduce the average relative mass error (ARME), a mass-conservation-based criterion that helps identify physically plausible simulations. We applied the model on dike ring 41 in the Netherlands, generating probabilistic flood maps that account for uncertainties in breach location and breach outflow hydrographs. The model was trained on 30 simulations, generated with Delft3D, and evaluated against unseen benchmark simulations from the Dutch national flood catalogue, achieving a critical success index (CSI) of 73.6 % while running 10 000 times faster than the numerical simulator. The proposed ARME is negatively correlated with the CSI, with a Spearman correlation coefficient of -0.7, making it a useful indicator of simulation plausibility when evaluating unseen case studies. We obtained probabilistic flood maps by running 10 000 different flooding scenarios on a computational mesh of 180 000 cells in approximately 10 h, with about half of the simulations classified as plausible based on the mass-conservation check. This framework offers a practical tool for rapid probabilistic flood hazard assessment and a way to prioritize detailed physical simulations, supporting more efficient and robust flood risk management.
...
Flood hazard maps are essential for protection and emergency plans, yet their probabilistic application is constrained by the computational cost of numerical models. Deep learning surrogates can provide orders of magnitude faster predictions, but their use for uncertainty quantification in realistic settings and their ability to incorporate hydraulic structures remain largely unexplored. Studying deep learning surrogates for probabilistic flood maps is non-trivial because of the lack of reference ground-truth data that might lead to misleading confidence in predictions. Moreover, hydraulic structures are challenging to include due to their generally unidimensional nature. In this work, we investigate the use of deep learning surrogates for realistic, large-scale flood simulations in case studies with hydraulic structures under diverse boundary conditions. To this end, we employ the multi-scale shallow-water-equations graph neural network (mSWE-GNN) that enjoys transferability to different boundary conditions and locations and whose graph-based architecture allows to represent structures such as canals, underpasses, and elevated elements as inputs. To address the lack of reference ground-truth data, we further introduce the average relative mass error (ARME), a mass-conservation-based criterion that helps identify physically plausible simulations. We applied the model on dike ring 41 in the Netherlands, generating probabilistic flood maps that account for uncertainties in breach location and breach outflow hydrographs. The model was trained on 30 simulations, generated with Delft3D, and evaluated against unseen benchmark simulations from the Dutch national flood catalogue, achieving a critical success index (CSI) of 73.6 % while running 10 000 times faster than the numerical simulator. The proposed ARME is negatively correlated with the CSI, with a Spearman correlation coefficient of -0.7, making it a useful indicator of simulation plausibility when evaluating unseen case studies. We obtained probabilistic flood maps by running 10 000 different flooding scenarios on a computational mesh of 180 000 cells in approximately 10 h, with about half of the simulations classified as plausible based on the mass-conservation check. This framework offers a practical tool for rapid probabilistic flood hazard assessment and a way to prioritize detailed physical simulations, supporting more efficient and robust flood risk management.
Modelling floods via graph neural networks
With applications to dike-breach floods
Flooding is one of the most frequent and destructive natural hazards, accounting for significant human and economic losses every year. Flood hazard mapping allows to identify vulnerable areas by estimating water depth, extent, and intensity under specific scenarios. These maps are created via numerical models as they provide accurate flood simulations. However, they are computationally expensive, particularly for overland flow at high resolution. Data-driven methods based on neural networks offer a promising alternative, delivering faster predictions while maintaining high accuracy.
To provide a comprehensive perspective on deep learning for flood mapping, we first reviewed the state of the art across different applications, considering a range of flood types, spatial scales, and deep learning architectures. Our analysis shows that deep learning methods generally outperform both traditional numerical approaches and conventional machine learning in terms of speed and accuracy. However, most existing models are tailored to individual case studies, neglect the dynamic evolution of flood waves, and cannot transfer to new topographic settings and boundary conditions not seen during training. Furthermore, current approaches struggle to incorporate physical principles, represent hydraulic structures, and provide physically consistent methods for validating outputs, particularly in the context of uncertainty quantification. Finally, we highlight that dike-breach floods remain largely under-represented in the literature, despite their high uncertainty stemming from flood defence failures.
In this thesis, we introduce Graph Neural Networks (GNNs) as hydraulics-inspired Surrogate models for simulating the spatio-temporal evolution of floods. While applicable to different flood types, our focus is on dike-breach floods due to their high uncertainty and particular relevance in the Netherlands and other low-lying areas. We build GNNs that are conceptually analogous to finite-volume methods used to solve the shallow water equations: finite-volume cells are treated as graph nodes, and flux exchanges are learned between adjacent cells by the model. The flood propagation in the proposed SWE-GNN model resembles hydraulics principles and enforces water to propagate only from cells with water. The model works in the same fashion as numerical solvers, auto-regressively predicting the evolution of the hydraulic states over time. By stacking multiple GNN layers, the model captures wider spatial dependencies without requiring small numerical time steps, theoretically needed for stability conditions. We also develop a multi-step ahead loss function combined with curriculum learning that further stabilizes long-term predictions.
We propose a multi-scale GNN formulation that models flood dynamics across different spatial resolutions, enabling the capture of both local and large-scale propagation processes. Time-varying boundary conditions are incorporated through ghost cells, removing the need for separate numerical solvers to initialize simulations. To enhance generalization across unseen unstructured meshes and reduce training data demands, we enforce invariance principles, ensuring the model is independent of coordinate rotations. This multi-scale approach proves both faster and more accurate than its single-scale counterpart. Our methods are validated on a suite of two-dimensional synthetic dike-breach simulations generated with a high-fidelity numerical solver. These datasets progressively increase in complexity by varying initial conditions, location of boundary conditions, size of the domain, computational mesh, and time-varying hydrographs used as boundary condition. Results demonstrate that the GNN generalizes well to unseen topographies, boundary configurations, and mesh configurations, without relying on inputs from numerical simulations. The models achieve a testing critical success index consistently higher than 70% in all datasets. The model also shows generalization to a real case study, dike ring 15 in the Netherlands, with only one fine-tuning simulation.
Finally, we extend the model to explicitly include hydraulic structures and to quantify uncertainty in flood hazard mapping of another real-world case study, dike ring 41 in the Netherlands. The framework is tested for large-scale uncertainty analysis with 10,000 scenarios. All simulations are completed in under 10 hours on a single GPU, corresponding to a speed-up of approximately 10,000 times with respect to the numerical solver, with over half of the scenarios maintaining plausible mass conservation. The combined scenarios are then used to produce probabilistic flood hazard maps, which assume equal likelihood of occurrence for each event. We also analyse the flood uncertainty for a given breach location and return period, showing that the model ensemble can provide better flooding estimates than the deterministic scenario.
This thesis highlights the potential of GNN-based surrogates for time-sensitive flood risk assessments under uncertainty. By demonstrating both accuracy and computational efficiency, it contributes to bridging the gap between complex hydraulic modelling and large-scale flood risk analysis. Despite being applied on dike-breach floods, the framework introduced in this thesis can readily be applied to fluvial and coastal floods without modifications. This open pathways for integrating surrogates into operational decision making and future flood resilience planning.
...
To provide a comprehensive perspective on deep learning for flood mapping, we first reviewed the state of the art across different applications, considering a range of flood types, spatial scales, and deep learning architectures. Our analysis shows that deep learning methods generally outperform both traditional numerical approaches and conventional machine learning in terms of speed and accuracy. However, most existing models are tailored to individual case studies, neglect the dynamic evolution of flood waves, and cannot transfer to new topographic settings and boundary conditions not seen during training. Furthermore, current approaches struggle to incorporate physical principles, represent hydraulic structures, and provide physically consistent methods for validating outputs, particularly in the context of uncertainty quantification. Finally, we highlight that dike-breach floods remain largely under-represented in the literature, despite their high uncertainty stemming from flood defence failures.
In this thesis, we introduce Graph Neural Networks (GNNs) as hydraulics-inspired Surrogate models for simulating the spatio-temporal evolution of floods. While applicable to different flood types, our focus is on dike-breach floods due to their high uncertainty and particular relevance in the Netherlands and other low-lying areas. We build GNNs that are conceptually analogous to finite-volume methods used to solve the shallow water equations: finite-volume cells are treated as graph nodes, and flux exchanges are learned between adjacent cells by the model. The flood propagation in the proposed SWE-GNN model resembles hydraulics principles and enforces water to propagate only from cells with water. The model works in the same fashion as numerical solvers, auto-regressively predicting the evolution of the hydraulic states over time. By stacking multiple GNN layers, the model captures wider spatial dependencies without requiring small numerical time steps, theoretically needed for stability conditions. We also develop a multi-step ahead loss function combined with curriculum learning that further stabilizes long-term predictions.
We propose a multi-scale GNN formulation that models flood dynamics across different spatial resolutions, enabling the capture of both local and large-scale propagation processes. Time-varying boundary conditions are incorporated through ghost cells, removing the need for separate numerical solvers to initialize simulations. To enhance generalization across unseen unstructured meshes and reduce training data demands, we enforce invariance principles, ensuring the model is independent of coordinate rotations. This multi-scale approach proves both faster and more accurate than its single-scale counterpart. Our methods are validated on a suite of two-dimensional synthetic dike-breach simulations generated with a high-fidelity numerical solver. These datasets progressively increase in complexity by varying initial conditions, location of boundary conditions, size of the domain, computational mesh, and time-varying hydrographs used as boundary condition. Results demonstrate that the GNN generalizes well to unseen topographies, boundary configurations, and mesh configurations, without relying on inputs from numerical simulations. The models achieve a testing critical success index consistently higher than 70% in all datasets. The model also shows generalization to a real case study, dike ring 15 in the Netherlands, with only one fine-tuning simulation.
Finally, we extend the model to explicitly include hydraulic structures and to quantify uncertainty in flood hazard mapping of another real-world case study, dike ring 41 in the Netherlands. The framework is tested for large-scale uncertainty analysis with 10,000 scenarios. All simulations are completed in under 10 hours on a single GPU, corresponding to a speed-up of approximately 10,000 times with respect to the numerical solver, with over half of the scenarios maintaining plausible mass conservation. The combined scenarios are then used to produce probabilistic flood hazard maps, which assume equal likelihood of occurrence for each event. We also analyse the flood uncertainty for a given breach location and return period, showing that the model ensemble can provide better flooding estimates than the deterministic scenario.
This thesis highlights the potential of GNN-based surrogates for time-sensitive flood risk assessments under uncertainty. By demonstrating both accuracy and computational efficiency, it contributes to bridging the gap between complex hydraulic modelling and large-scale flood risk analysis. Despite being applied on dike-breach floods, the framework introduced in this thesis can readily be applied to fluvial and coastal floods without modifications. This open pathways for integrating surrogates into operational decision making and future flood resilience planning.
...
Flooding is one of the most frequent and destructive natural hazards, accounting for significant human and economic losses every year. Flood hazard mapping allows to identify vulnerable areas by estimating water depth, extent, and intensity under specific scenarios. These maps are created via numerical models as they provide accurate flood simulations. However, they are computationally expensive, particularly for overland flow at high resolution. Data-driven methods based on neural networks offer a promising alternative, delivering faster predictions while maintaining high accuracy.
To provide a comprehensive perspective on deep learning for flood mapping, we first reviewed the state of the art across different applications, considering a range of flood types, spatial scales, and deep learning architectures. Our analysis shows that deep learning methods generally outperform both traditional numerical approaches and conventional machine learning in terms of speed and accuracy. However, most existing models are tailored to individual case studies, neglect the dynamic evolution of flood waves, and cannot transfer to new topographic settings and boundary conditions not seen during training. Furthermore, current approaches struggle to incorporate physical principles, represent hydraulic structures, and provide physically consistent methods for validating outputs, particularly in the context of uncertainty quantification. Finally, we highlight that dike-breach floods remain largely under-represented in the literature, despite their high uncertainty stemming from flood defence failures.
In this thesis, we introduce Graph Neural Networks (GNNs) as hydraulics-inspired Surrogate models for simulating the spatio-temporal evolution of floods. While applicable to different flood types, our focus is on dike-breach floods due to their high uncertainty and particular relevance in the Netherlands and other low-lying areas. We build GNNs that are conceptually analogous to finite-volume methods used to solve the shallow water equations: finite-volume cells are treated as graph nodes, and flux exchanges are learned between adjacent cells by the model. The flood propagation in the proposed SWE-GNN model resembles hydraulics principles and enforces water to propagate only from cells with water. The model works in the same fashion as numerical solvers, auto-regressively predicting the evolution of the hydraulic states over time. By stacking multiple GNN layers, the model captures wider spatial dependencies without requiring small numerical time steps, theoretically needed for stability conditions. We also develop a multi-step ahead loss function combined with curriculum learning that further stabilizes long-term predictions.
We propose a multi-scale GNN formulation that models flood dynamics across different spatial resolutions, enabling the capture of both local and large-scale propagation processes. Time-varying boundary conditions are incorporated through ghost cells, removing the need for separate numerical solvers to initialize simulations. To enhance generalization across unseen unstructured meshes and reduce training data demands, we enforce invariance principles, ensuring the model is independent of coordinate rotations. This multi-scale approach proves both faster and more accurate than its single-scale counterpart. Our methods are validated on a suite of two-dimensional synthetic dike-breach simulations generated with a high-fidelity numerical solver. These datasets progressively increase in complexity by varying initial conditions, location of boundary conditions, size of the domain, computational mesh, and time-varying hydrographs used as boundary condition. Results demonstrate that the GNN generalizes well to unseen topographies, boundary configurations, and mesh configurations, without relying on inputs from numerical simulations. The models achieve a testing critical success index consistently higher than 70% in all datasets. The model also shows generalization to a real case study, dike ring 15 in the Netherlands, with only one fine-tuning simulation.
Finally, we extend the model to explicitly include hydraulic structures and to quantify uncertainty in flood hazard mapping of another real-world case study, dike ring 41 in the Netherlands. The framework is tested for large-scale uncertainty analysis with 10,000 scenarios. All simulations are completed in under 10 hours on a single GPU, corresponding to a speed-up of approximately 10,000 times with respect to the numerical solver, with over half of the scenarios maintaining plausible mass conservation. The combined scenarios are then used to produce probabilistic flood hazard maps, which assume equal likelihood of occurrence for each event. We also analyse the flood uncertainty for a given breach location and return period, showing that the model ensemble can provide better flooding estimates than the deterministic scenario.
This thesis highlights the potential of GNN-based surrogates for time-sensitive flood risk assessments under uncertainty. By demonstrating both accuracy and computational efficiency, it contributes to bridging the gap between complex hydraulic modelling and large-scale flood risk analysis. Despite being applied on dike-breach floods, the framework introduced in this thesis can readily be applied to fluvial and coastal floods without modifications. This open pathways for integrating surrogates into operational decision making and future flood resilience planning.
To provide a comprehensive perspective on deep learning for flood mapping, we first reviewed the state of the art across different applications, considering a range of flood types, spatial scales, and deep learning architectures. Our analysis shows that deep learning methods generally outperform both traditional numerical approaches and conventional machine learning in terms of speed and accuracy. However, most existing models are tailored to individual case studies, neglect the dynamic evolution of flood waves, and cannot transfer to new topographic settings and boundary conditions not seen during training. Furthermore, current approaches struggle to incorporate physical principles, represent hydraulic structures, and provide physically consistent methods for validating outputs, particularly in the context of uncertainty quantification. Finally, we highlight that dike-breach floods remain largely under-represented in the literature, despite their high uncertainty stemming from flood defence failures.
In this thesis, we introduce Graph Neural Networks (GNNs) as hydraulics-inspired Surrogate models for simulating the spatio-temporal evolution of floods. While applicable to different flood types, our focus is on dike-breach floods due to their high uncertainty and particular relevance in the Netherlands and other low-lying areas. We build GNNs that are conceptually analogous to finite-volume methods used to solve the shallow water equations: finite-volume cells are treated as graph nodes, and flux exchanges are learned between adjacent cells by the model. The flood propagation in the proposed SWE-GNN model resembles hydraulics principles and enforces water to propagate only from cells with water. The model works in the same fashion as numerical solvers, auto-regressively predicting the evolution of the hydraulic states over time. By stacking multiple GNN layers, the model captures wider spatial dependencies without requiring small numerical time steps, theoretically needed for stability conditions. We also develop a multi-step ahead loss function combined with curriculum learning that further stabilizes long-term predictions.
We propose a multi-scale GNN formulation that models flood dynamics across different spatial resolutions, enabling the capture of both local and large-scale propagation processes. Time-varying boundary conditions are incorporated through ghost cells, removing the need for separate numerical solvers to initialize simulations. To enhance generalization across unseen unstructured meshes and reduce training data demands, we enforce invariance principles, ensuring the model is independent of coordinate rotations. This multi-scale approach proves both faster and more accurate than its single-scale counterpart. Our methods are validated on a suite of two-dimensional synthetic dike-breach simulations generated with a high-fidelity numerical solver. These datasets progressively increase in complexity by varying initial conditions, location of boundary conditions, size of the domain, computational mesh, and time-varying hydrographs used as boundary condition. Results demonstrate that the GNN generalizes well to unseen topographies, boundary configurations, and mesh configurations, without relying on inputs from numerical simulations. The models achieve a testing critical success index consistently higher than 70% in all datasets. The model also shows generalization to a real case study, dike ring 15 in the Netherlands, with only one fine-tuning simulation.
Finally, we extend the model to explicitly include hydraulic structures and to quantify uncertainty in flood hazard mapping of another real-world case study, dike ring 41 in the Netherlands. The framework is tested for large-scale uncertainty analysis with 10,000 scenarios. All simulations are completed in under 10 hours on a single GPU, corresponding to a speed-up of approximately 10,000 times with respect to the numerical solver, with over half of the scenarios maintaining plausible mass conservation. The combined scenarios are then used to produce probabilistic flood hazard maps, which assume equal likelihood of occurrence for each event. We also analyse the flood uncertainty for a given breach location and return period, showing that the model ensemble can provide better flooding estimates than the deterministic scenario.
This thesis highlights the potential of GNN-based surrogates for time-sensitive flood risk assessments under uncertainty. By demonstrating both accuracy and computational efficiency, it contributes to bridging the gap between complex hydraulic modelling and large-scale flood risk analysis. Despite being applied on dike-breach floods, the framework introduced in this thesis can readily be applied to fluvial and coastal floods without modifications. This open pathways for integrating surrogates into operational decision making and future flood resilience planning.
Journal article
(2025)
-
Roberto Bentivoglio, Elvin Isufi, Sebastiaan Nicolas Jonkman, Riccardo Taormina
Deep-learning-based surrogate models represent a powerful alternative to numerical models for speeding up flood mapping while preserving accuracy. In particular, solutions based on hydraulic-based graph neural networks (SWE-GNNs) enable transferability to domains not used for training and allow the inclusion of physical constraints. However, these models are limited due to four main aspects. First, they cannot model rapid differences in flow propagation speeds; secondly, they can face instabilities during training when using a large number of layers, needed for effective modelling; third, they cannot accommodate time-varying boundary conditions; and fourth, they require initial conditions from a numerical solver. To address these issues, we propose a multi-scale hydraulic-based graph neural network (mSWE-GNN) that models the flood at different resolutions and propagation speeds. We include time-varying boundary conditions via ghost cells, which enforce the solution at the domain’s boundary and drop the need for a numerical solver for the initial conditions. To improve generalization over unseen meshes and reduce the data demand, we use invariance principles and make the inputs independent from coordinates' rotations. Numerical results applied to dike-breach floods show that the model predicts the full spatio-temporal simulation of the flood over unseen irregular meshes, topographies, and time-varying boundary conditions, with mean absolute errors in time of 0.05 m for water depths and 0.003 m2 s−1 for unit discharges. We further corroborate the mSWE-GNN in a realistic case study in the Netherlands and show generalization capabilities with only one fine-tuning sample, with mean absolute errors of 0.12 m for water depth, a critical success index for a water depth threshold of 0.05 m of 87.68 %, and speed-ups of over 700 times. Overall, the approach opens up several avenues for probabilistic analyses of realistic configurations and flood scenarios.
...
Deep-learning-based surrogate models represent a powerful alternative to numerical models for speeding up flood mapping while preserving accuracy. In particular, solutions based on hydraulic-based graph neural networks (SWE-GNNs) enable transferability to domains not used for training and allow the inclusion of physical constraints. However, these models are limited due to four main aspects. First, they cannot model rapid differences in flow propagation speeds; secondly, they can face instabilities during training when using a large number of layers, needed for effective modelling; third, they cannot accommodate time-varying boundary conditions; and fourth, they require initial conditions from a numerical solver. To address these issues, we propose a multi-scale hydraulic-based graph neural network (mSWE-GNN) that models the flood at different resolutions and propagation speeds. We include time-varying boundary conditions via ghost cells, which enforce the solution at the domain’s boundary and drop the need for a numerical solver for the initial conditions. To improve generalization over unseen meshes and reduce the data demand, we use invariance principles and make the inputs independent from coordinates' rotations. Numerical results applied to dike-breach floods show that the model predicts the full spatio-temporal simulation of the flood over unseen irregular meshes, topographies, and time-varying boundary conditions, with mean absolute errors in time of 0.05 m for water depths and 0.003 m2 s−1 for unit discharges. We further corroborate the mSWE-GNN in a realistic case study in the Netherlands and show generalization capabilities with only one fine-tuning sample, with mean absolute errors of 0.12 m for water depth, a critical success index for a water depth threshold of 0.05 m of 87.68 %, and speed-ups of over 700 times. Overall, the approach opens up several avenues for probabilistic analyses of realistic configurations and flood scenarios.
Journal article
(2023)
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Cesar A.F. do Lago, Marcio H. Giacomoni, Roberto Bentivoglio, Riccardo Taormina, Marcus N. Gomes, Eduardo M. Mendiondo
Two-dimensional hydrodynamic models are computationally expensive. This drawback can limit their application to solving problems requiring real-time predictions or several simulation runs. Although the literature presented improvements in using Deep Learning as an alternative to hydrodynamic models, Artificial Neural Networks applications for flood prediction cannot satisfactorily predict floods for areas outside the training datasets with different boundary conditions. In this paper, we used a conditional generative adversarial network (cGAN) aiming to generalize flood predictions in catchments not included in the training process. The proposed method, called cGAN-Flood, uses two cGAN models to solve a rain-on-grid problem by first identifying wet cells and then estimating the water depths. The cGANs were trained using HEC-RAS outputs as ground truth. cGAN-Flood distributes a target flood volume (vt) in a given catchment, which can be calculated via water balance from hydrological simulations. Our approach was trained on ten and tested on five urban catchments with distinct characteristics. The cGAN-Flood was compared to HEC-RAS for different rainfall magnitudes and surface roughness. We also compared our approach to the Weighted Cellular Automata 2D (WCA2D), a rapid flood model (RFM) used for rain-on-grid simulations. Our method successfully predicted water depths in the testing areas, showing that cGAN-Flood could generalize to different locations. However, cGAN-Flood tended to underestimate depths in channels in some areas for events with a small peak of precipitation intensity. cGAN-Flood was 50 and 250 times faster than WCA2D and HEC-RAS, respectively. Due to its computational efficiency and accuracy, we suggest that cGAN-Flood can be applied when fast simulations are necessary, and it can be a viable modeling solution for flood forecasts in large-scale watersheds.
...
Two-dimensional hydrodynamic models are computationally expensive. This drawback can limit their application to solving problems requiring real-time predictions or several simulation runs. Although the literature presented improvements in using Deep Learning as an alternative to hydrodynamic models, Artificial Neural Networks applications for flood prediction cannot satisfactorily predict floods for areas outside the training datasets with different boundary conditions. In this paper, we used a conditional generative adversarial network (cGAN) aiming to generalize flood predictions in catchments not included in the training process. The proposed method, called cGAN-Flood, uses two cGAN models to solve a rain-on-grid problem by first identifying wet cells and then estimating the water depths. The cGANs were trained using HEC-RAS outputs as ground truth. cGAN-Flood distributes a target flood volume (vt) in a given catchment, which can be calculated via water balance from hydrological simulations. Our approach was trained on ten and tested on five urban catchments with distinct characteristics. The cGAN-Flood was compared to HEC-RAS for different rainfall magnitudes and surface roughness. We also compared our approach to the Weighted Cellular Automata 2D (WCA2D), a rapid flood model (RFM) used for rain-on-grid simulations. Our method successfully predicted water depths in the testing areas, showing that cGAN-Flood could generalize to different locations. However, cGAN-Flood tended to underestimate depths in channels in some areas for events with a small peak of precipitation intensity. cGAN-Flood was 50 and 250 times faster than WCA2D and HEC-RAS, respectively. Due to its computational efficiency and accuracy, we suggest that cGAN-Flood can be applied when fast simulations are necessary, and it can be a viable modeling solution for flood forecasts in large-scale watersheds.
Journal article
(2023)
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Bulat Kerimov, Roberto Bentivoglio, Alexander Garzón, Elvin Isufi, Franz Tscheikner-Gratl, David Bernhard Steffelbauer, Riccardo Taormina
Metamodels accurately reproduce the output of physics-based hydraulic models with a significant reduction in simulation times. They are widely employed in water distribution system (WDS) analysis since they enable computationally expensive applications in the design, control, and optimisation of water networks. Recent machine-learning-based metamodels grant improved fidelity and speed; however, they are only applicable to the water network they were trained on. To address this issue, we investigate graph neural networks (GNNs) as metamodels for WDSs. GNNs leverage the networked structure of WDS by learning shared coefficients and thus offering the potential of transferability. This work evaluates the suitability of GNNs as metamodels for estimating nodal pressures in steady-state EPANET simulations. We first compare the effectiveness of GNN metamodels against multi-layer perceptrons (MLPs) on several benchmark WDSs. Then, we explore the transferability of GNNs by training them concurrently on multiple WDSs. For each configuration, we calculate model accuracy and speedups with respect to the original numerical model. GNNs perform similarly to MLPs in terms of accuracy and take longer to execute but may still provide substantial speedup. Our preliminary results indicate that GNNs can learn shared representations across networks, although assessing the feasibility of truly general metamodels requires further work.
...
Metamodels accurately reproduce the output of physics-based hydraulic models with a significant reduction in simulation times. They are widely employed in water distribution system (WDS) analysis since they enable computationally expensive applications in the design, control, and optimisation of water networks. Recent machine-learning-based metamodels grant improved fidelity and speed; however, they are only applicable to the water network they were trained on. To address this issue, we investigate graph neural networks (GNNs) as metamodels for WDSs. GNNs leverage the networked structure of WDS by learning shared coefficients and thus offering the potential of transferability. This work evaluates the suitability of GNNs as metamodels for estimating nodal pressures in steady-state EPANET simulations. We first compare the effectiveness of GNN metamodels against multi-layer perceptrons (MLPs) on several benchmark WDSs. Then, we explore the transferability of GNNs by training them concurrently on multiple WDSs. For each configuration, we calculate model accuracy and speedups with respect to the original numerical model. GNNs perform similarly to MLPs in terms of accuracy and take longer to execute but may still provide substantial speedup. Our preliminary results indicate that GNNs can learn shared representations across networks, although assessing the feasibility of truly general metamodels requires further work.
Journal article
(2023)
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Roberto Bentivoglio, Elvin Isufi, Sebastiaan Nicolas Jonkman, Riccardo Taormina
Numerical modelling is a reliable tool for flood simulations, but accurate solutions are computationally expensive. In recent years, researchers have explored data-driven methodologies based on neural networks to overcome this limitation. However, most models are only used for a specific case study and disregard the dynamic evolution of the flood wave. This limits their generalizability to topographies that the model was not trained on and in time-dependent applications. In this paper, we introduce shallow water equation–graph neural network (SWE–GNN), a hydraulics-inspired surrogate model based on GNNs that can be used for rapid spatio-temporal flood modelling. The model exploits the analogy between finite-volume methods used to solve SWEs and GNNs. For a computational mesh, we create a graph by considering finite-volume cells as nodes and adjacent cells as being connected by edges. The inputs are determined by the topographical properties of the domain and the initial hydraulic conditions. The GNN then determines how fluxes are exchanged between cells via a learned local function. We overcome the time-step constraints by stacking multiple GNN layers, which expand the considered space instead of increasing the time resolution. We also propose a multi-step-ahead loss function along with a curriculum learning strategy to improve the stability and performance. We validate this approach using a dataset of two-dimensional dike breach flood simulations in randomly generated digital elevation models generated with a high-fidelity numerical solver. The SWE–GNN model predicts the spatio-temporal evolution of the flood for unseen topographies with mean average errors in time of 0.04 m for water depths and 0.004 m2 s−1 for unit discharges. Moreover, it generalizes well to unseen breach locations, bigger domains, and longer periods of time compared to those of the training set, outperforming other deep-learning models. On top of this, SWE–GNN has a computational speed-up of up to 2 orders of magnitude faster than the numerical solver. Our framework opens the doors to a new approach to replace numerical solvers in time-sensitive applications with spatially dependent uncertainties.
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Numerical modelling is a reliable tool for flood simulations, but accurate solutions are computationally expensive. In recent years, researchers have explored data-driven methodologies based on neural networks to overcome this limitation. However, most models are only used for a specific case study and disregard the dynamic evolution of the flood wave. This limits their generalizability to topographies that the model was not trained on and in time-dependent applications. In this paper, we introduce shallow water equation–graph neural network (SWE–GNN), a hydraulics-inspired surrogate model based on GNNs that can be used for rapid spatio-temporal flood modelling. The model exploits the analogy between finite-volume methods used to solve SWEs and GNNs. For a computational mesh, we create a graph by considering finite-volume cells as nodes and adjacent cells as being connected by edges. The inputs are determined by the topographical properties of the domain and the initial hydraulic conditions. The GNN then determines how fluxes are exchanged between cells via a learned local function. We overcome the time-step constraints by stacking multiple GNN layers, which expand the considered space instead of increasing the time resolution. We also propose a multi-step-ahead loss function along with a curriculum learning strategy to improve the stability and performance. We validate this approach using a dataset of two-dimensional dike breach flood simulations in randomly generated digital elevation models generated with a high-fidelity numerical solver. The SWE–GNN model predicts the spatio-temporal evolution of the flood for unseen topographies with mean average errors in time of 0.04 m for water depths and 0.004 m2 s−1 for unit discharges. Moreover, it generalizes well to unseen breach locations, bigger domains, and longer periods of time compared to those of the training set, outperforming other deep-learning models. On top of this, SWE–GNN has a computational speed-up of up to 2 orders of magnitude faster than the numerical solver. Our framework opens the doors to a new approach to replace numerical solvers in time-sensitive applications with spatially dependent uncertainties.
Deep learning methods for flood mapping
A review of existing applications and future research directions
Deep learning techniques have been increasingly used in flood management to overcome the limitations of accurate, yet slow, numerical models and to improve the results of traditional methods for flood mapping. In this paper, we review 58 recent publications to outline the state of the art of the field, identify knowledge gaps, and propose future research directions. The review focuses on the type of deep learning models used for various flood mapping applications, the flood types considered, the spatial scale of the studied events, and the data used for model development. The results show that models based on convolutional layers are usually more accurate, as they leverage inductive biases to better process the spatial characteristics of the flooding events. Models based on fully connected layers, instead, provide accurate results when coupled with other statistical models. Deep learning models showed increased accuracy when compared to traditional approaches and increased speed when compared to numerical methods. While there exist several applications in flood susceptibility, inundation, and hazard mapping, more work is needed to understand how deep learning can assist in real-time flood warning during an emergency and how it can be employed to estimate flood risk. A major challenge lies in developing deep learning models that can generalize to unseen case studies. Furthermore, all reviewed models and their outputs are deterministic, with limited considerations for uncertainties in outcomes and probabilistic predictions. The authors argue that these identified gaps can be addressed by exploiting recent fundamental advancements in deep learning or by taking inspiration from developments in other applied areas. Models based on graph neural networks and neural operators can work with arbitrarily structured data and thus should be capable of generalizing across different case studies and could account for complex interactions with the natural and built environment. Physics-based deep learning can be used to preserve the underlying physical equations resulting in more reliable speed-up alternatives for numerical models. Similarly, probabilistic models can be built by resorting to deep Gaussian processes or Bayesian neural networks.
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Deep learning techniques have been increasingly used in flood management to overcome the limitations of accurate, yet slow, numerical models and to improve the results of traditional methods for flood mapping. In this paper, we review 58 recent publications to outline the state of the art of the field, identify knowledge gaps, and propose future research directions. The review focuses on the type of deep learning models used for various flood mapping applications, the flood types considered, the spatial scale of the studied events, and the data used for model development. The results show that models based on convolutional layers are usually more accurate, as they leverage inductive biases to better process the spatial characteristics of the flooding events. Models based on fully connected layers, instead, provide accurate results when coupled with other statistical models. Deep learning models showed increased accuracy when compared to traditional approaches and increased speed when compared to numerical methods. While there exist several applications in flood susceptibility, inundation, and hazard mapping, more work is needed to understand how deep learning can assist in real-time flood warning during an emergency and how it can be employed to estimate flood risk. A major challenge lies in developing deep learning models that can generalize to unseen case studies. Furthermore, all reviewed models and their outputs are deterministic, with limited considerations for uncertainties in outcomes and probabilistic predictions. The authors argue that these identified gaps can be addressed by exploiting recent fundamental advancements in deep learning or by taking inspiration from developments in other applied areas. Models based on graph neural networks and neural operators can work with arbitrarily structured data and thus should be capable of generalizing across different case studies and could account for complex interactions with the natural and built environment. Physics-based deep learning can be used to preserve the underlying physical equations resulting in more reliable speed-up alternatives for numerical models. Similarly, probabilistic models can be built by resorting to deep Gaussian processes or Bayesian neural networks.
Journal article
(2021)
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Elisabetta Persi , Gabriella Petaccia, Stefano Sibilla , Roberto Bentivoglio, Aronne Armanini
An advection-diffusion model is proposed to simulate large wood transport during high flows. The mathematical model is derived from the wood mass balance, taking into consideration both the wood mass concentration and the log orientation, which affects log transport and, most importantly, wood accumulation. Focusing on wood mass transport, the advection-diffusion equation is implemented in a hydrodynamic model to provide a one-way coupled solution of the flow and of the floating wood mass. The model is tested on a large series of flume experiments, involving at least 30 logs and different control parameters (flow Froude number, log length, diameter, release point). The validation through the experimental data shows that the proposed model can predict the correct displacement of the most probable position of the logs and to simulate with a sufficient accuracy the planar diffusion of the wooden mass. Transversal wood distribution is more accurate than the streamwise one, indicating that a higher control on the longitudinal diffusion needs to be implemented.
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An advection-diffusion model is proposed to simulate large wood transport during high flows. The mathematical model is derived from the wood mass balance, taking into consideration both the wood mass concentration and the log orientation, which affects log transport and, most importantly, wood accumulation. Focusing on wood mass transport, the advection-diffusion equation is implemented in a hydrodynamic model to provide a one-way coupled solution of the flow and of the floating wood mass. The model is tested on a large series of flume experiments, involving at least 30 logs and different control parameters (flow Froude number, log length, diameter, release point). The validation through the experimental data shows that the proposed model can predict the correct displacement of the most probable position of the logs and to simulate with a sufficient accuracy the planar diffusion of the wooden mass. Transversal wood distribution is more accurate than the streamwise one, indicating that a higher control on the longitudinal diffusion needs to be implemented.