Abstract. 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.

Abstract. Deep Learning techniques have been increasingly used in flood risk 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 45 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. Traditional 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 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 and sites. 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. Neural operators can also speed up numerical models while preserving the underlying physical equations and could thus be used for reliable real-time warning. Similarly, probabilistic models can be built by resorting to Deep Gaussian Processes.

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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Abstract. 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 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.

Abstract. Numerical modelling is a reliable tool for flood simulations, but accurate solutions are computationally expensive. In the recent years, researchers have explored data-driven methodologies based on neural networks to overcome this limitation. However, most models are used only 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 SWE-GNN, a hydraulics-inspired surrogate model based on Graph Neural Networks (GNN) that can be used for rapid spatio-temporal flood modelling. The model exploits the analogy between finite volume methods, used to solve the shallow water equations (SWE), and GNNs. For a computational mesh, we create a graph by considering finite-volume cells as nodes and adjacent cells as 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 on randomly-generated digital elevation models, generated with a highfidelity numerical solver. The SWE-GNN model predicts the spatio-temporal evolution of the flood for unseen topographies with a mean average error in time of 0.04 m for water depths and 0.004 m2/s for unit discharges. Moreover, it generalizes well to unseen breach locations, bigger domains, and over longer periods of time, outperforming other deep learning models. On top of this, SWE-GNN has a computational speedup of up to two orders of magnitude faster than the numerical solver. Our framework opens the doors to a new approach for replacing numerical solvers in time-sensitive applications with spatially-dependant uncertainties.

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