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 (v_t) 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.

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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.@en

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.

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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.@en

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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