Grid adaptive reduced-order model of fluid flow based on graph convolutional neural network

Abstract

In the interdisciplinary field of data-driven models and computational fluid mechanics, the reduced-order model for flow field prediction is mainly constructed by a convolutional neural network (CNN) in recent years. However, the standard CNN is only applicable to data with Euclidean spatial structure, while data with non-Euclidean properties can only be convolved after pixelization, which usually leads to decreased data accuracy. In this work, a novel data-driven framework based on graph convolution network (GCN) is proposed to allow the convolution operator to predict fluid dynamics on non-uniform structured or unstructured mesh data. This is achieved by the fact that the graph data inherit the spatial characteristics of the mesh and by the message passing mechanism of GCN. The conversion method from the form of mesh data to graph data and the operation mechanism of GCN are clarified. Moreover, additional relevance features and weight loss function of the dataset are also investigated to improve the model performance. The model learns an end-to-end mapping between the mesh spatial features and the physical flow field. Through our studies of various cases of internal flow, it is shown that the proposed GCN-based model offers excellent adaptability to non-uniformly distributed mesh data, while also achieving a high accuracy and three-order speedup compared with numerical simulation. Our framework generalizes the graph convolution network to flow field prediction and opens the door to further extending GCN to most existing data-driven architectures of fluid dynamics in the future.

Prediction of Transonic Flow over Cascades via Graph Embedding Methods on Large-Scale Point Clouds

“…However, for the irregular flow field depicted in Figure 1, conventional CNNbased methods may not be well-suited, as ordinary CNN approaches are constrained in generalizing to unstructured data because of the challenge of selecting a fixed convolution kernel that can effectively accommodate the various grid sizes, shapes, and irregular boundaries. Moreover, GCN effectively captures both topological structures [25] and flow tures [26]. Additionally, GCN leverages sparse matrices for computation, enablin handling of larger matrices and accommodating extensive discrete flow-field p Meanwhile, convolutional networks aggregate features from neighboring nodes, op ing the utilization of topological information between these nodes [27].…”

“…Economon et al [28 bined traditional GCN with CFD simulations, which significantly accelerated pred speed. To address non-Euclidean flow problems, Wang et al [29] integrated GCN traditional numerical solvers and proposed the FlowGCN solver, which signifi speeded up the convergence of the entire program and secured accurate predictions et al [26] proposed a data-driven flow prediction framework, GraphSAGE, based o basic architecture of GCN. This framework learned potential features by samplin aggregating features from the local neighborhoods of vertices, demonstrating good a ability to non-uniformly distributed grid data.…”

“…Ying et al [33] analyzed the impact of node features and the linking proc node information aggregation on model predictions and proposed GNNExplainer, identified crucial subgraph structures and node features within GNN predictions, de strating a general and model-agnostic property. SubgraphX [34] focused on the sub tures of the graph, interpreting GNN by exploring and identifying significant subgr GNN Prediction Interpreter (GPI) [35] studied the correlation between node feature GNN predictions and elucidated the impact of node features on GNN predic Moreover, GCN effectively captures both topological structures [25] and flow features [26]. Additionally, GCN leverages sparse matrices for computation, enabling the handling of larger matrices and accommodating extensive discrete flow-field points.…”

Rapid spatio-temporal flood modelling via hydraulics-based graph neural networks

“…GNNs generalize convolutional neural networks to irregular domains such as graphs and have shown promising results for fluid dynamics (e.g. Lino et al, 2021;Peng et al, 2022) and partial differential equations (e.g. Brandstetter et al, 2022;Horie and Mitsume, 2022).…”

Rapid Spatio-Temporal Flood Modelling via Hydraulics-Based Graph Neural Networks

“…To overcome this limitation, we propose SWE-GNN, a deep learning model merging graph neural networks (GNN) with the finite-volume methods used to solve the SWE. GNNs generalize convolutional neural networks to irregular domains such as graphs and have shown promising results for fluid dynamics (e.g., Lino et al, 2021;Peng et al, 2022) and partial differential equations (e.g., Brandstetter et al, 2022;Horie and Mitsume, 2022). Hence, developing GNNs that follow the SWE equations is not only more physically interpretable but also allows better generalization abilities to unseen flood evolution, unseen breach location and unseen topographies.…”