Classical approaches for flood prediction apply numerical methods for the solution of partial differential equations that capture the physics of inundation processes (e.g., the 2D Shallow Water equations). However, traditional inundation models are still unable to satisfy the requirements of many relevant applications, including early-warning systems, high-resolution (or large spatial domain) simulations, and robust inference over distributions of inputs (e.g., rainfall events). Machine learning (ML) approaches are a promising alternative to physics-based models due to their ability to efficiently capture correlations between relevant inputs and outputs in a data-driven fashion. In particular, once trained, ML models can be tested/deployed much more efficiently than classical approaches. Yet, few ML-based solutions for spatio-temporal flood prediction have been developed, and their reliability/accuracy is poorly understood. In this paper, we propose FloodGNN-GRU, a spatio-temporal flood prediction model that combines a graph neural network (GNN) and a gated recurrent unit (GRU) architecture. Compared to existing approaches, FloodGNN-GRU (i) employs a graph-based model (GNN); (ii) operates on both spatial and temporal dimensions; and (iii) processes the water flow velocities as vector features, instead of scalar features. We evaluate FloodGNN-GRU using a LISFLOOD-FP simulation of Hurricane Harvey (2017) in Houston, Texas. Our results, based on several metrics, show that FloodGNN-GRU outperforms several data-driven alternatives in terms of accuracy. Moreover, our approach can be trained 100x faster and tested 1000x faster than the time required to run a comparable simulation. These findings illustrate the potential of ML-based methods to efficiently emulate physics-based inundation models, especially for short-term predictions.

Compressible anisothermal flows, which are commonly found in industrial settings such as combustion chambers and heat exchangers, are characterized by significant variations in density, viscosity, and heat conductivity with temperature. These variations lead to a strong interaction between the temperature and velocity fields that impacts the near-wall profiles of both quantities. Wall-modeled large-eddy simulations (LESs) rely on a wall model to provide a boundary condition, for example, the shear stress and the heat flux that accurately represents this interaction despite the use of coarse cells near the wall, and thereby achieve a good balance between computational cost and accuracy. In this article, the use of graph neural networks for wall modeling in LES is assessed for compressible anisothermal flow. Graph neural networks are a type of machine learning model that can learn from data and operate directly on complex unstructured meshes. Previous work has shown the effectiveness of graph neural network wall modeling for isothermal incompressible flows. This article develops the graph neural network architecture and training to extend their applicability to compressible anisothermal flows. The model is trained and tested a priori using a database of both incompressible isothermal and compressible anisothermal flows. The model is finally tested a posteriori for the wall-modeled LES of a channel flow and a turbine blade, both of which were not seen during training.

As the Reynolds number increases, the large-eddy simulation (LES) of complex flows becomes increasingly intractable because near-wall turbulent structures become increasingly small. Wall modeling reduces the computational requirements of LES by enabling the use of coarser cells at the walls. This paper presents a machine-learning methodology to develop data-driven wall-shear-stress models that can directly operate, a posteriori, on the unstructured grid of the simulation. The model architecture is based on graph neural networks. The model is trained on a database which includes fully developed boundary layers, adverse pressure gradients, separated boundary layers, and laminar–turbulent transition. The relevance of the trained model is verified a posteriori for the simulation of a channel flow, a backward-facing step and a linear blade cascade.

Physics-informed machine learning (PIML) has emerged as a promising new approach for simulating complex physical and biological systems that are governed by complex multiscale processes for which some data are also available. In some instances, the objective is to discover part of the hidden physics from the available data, and PIML has been shown to be particularly effective for such problems for which conventional methods may fail. Unlike commercial machine learning where training of deep neural networks requires big data, in PIML big data are not available. Instead, we can train such networks from additional information obtained by employing the physical laws and evaluating them at random points in the space–time domain. Such PIML integrates multimodality and multifidelity data with mathematical models, and implements them using neural networks or graph networks. Here, we review some of the prevailing trends in embedding physics into machine learning, using physics-informed neural networks (PINNs) based primarily on feed-forward neural networks and automatic differentiation. For more complex systems or systems of systems and unstructured data, graph neural networks (GNNs) present some distinct advantages, and here we review how physics-informed learning can be accomplished with GNNs based on graph exterior calculus to construct differential operators; we refer to these architectures as physics-informed graph networks (PIGNs). We present representative examples for both forward and inverse problems and discuss what advances are needed to scale up PINNs, PIGNs and more broadly GNNs for large-scale engineering problems.