# Flow Completion Network: Inferring the Fluid Dynamics from Incomplete Flow Information using Graph Neural Networks

arXiv: https://arxiv.org/abs/2205.04739 · HTML: https://mlsanity.com/paper/2205.04739/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 23 references that are in the map.
- First posted on arXiv 10 May 2022.

## Builds on (most cited first, 9 of 9)

- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [SegNet: A Deep Convolutional Encoder-Decoder Architecture for Image Segmentation](https://mlsanity.com/paper/1511.00561/) (2015)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Prediction of Aerodynamic Flow Fields Using Convolutional Neural Networks](https://mlsanity.com/paper/1905.13166/) (2019)
- [Deep Learning of Vortex Induced Vibrations](https://mlsanity.com/paper/1808.08952/) (2018)
- [Global field reconstruction from sparse sensors with Voronoi tessellation-assisted deep learning](https://mlsanity.com/paper/2101.00554/) (2021)
- [Graph Convolutional Neural Networks for Body Force Prediction](https://mlsanity.com/paper/2012.02232/) (2020)
- [Spatial-temporal wind field prediction by Artificial Neural Networks](https://mlsanity.com/paper/1712.05293/) (2017)

## Built on by (most cited first, 13 of 13)

- [A Finite Element-Inspired Hypergraph Neural Network: Application to Fluid Dynamics Simulations](https://mlsanity.com/paper/2212.14545/) (2022)
- [A review of graph neural network applications in mechanics-related domains](https://mlsanity.com/paper/2407.11060/) (2024)
- [Machine learning for modelling unstructured grid data in computational physics: a review](https://mlsanity.com/paper/2502.09346/) (2025)
- [Mesh-based Super-Resolution of Fluid Flows with Multiscale Graph Neural Networks](https://mlsanity.com/paper/2409.07769/) (2024)
- [Predicting fluid-structure interaction with graph neural networks](https://mlsanity.com/paper/2210.04193/) (2022)
- [FD-Bench: A Modular and Fair Benchmark for Data-driven Fluid Simulation](https://mlsanity.com/paper/2505.20349/) (2025)
- [A graph neural network surrogate model for mesh-based crashworthiness prediction of vehicle panel components](https://mlsanity.com/paper/2503.17386/) (2025)
- [Invariant Control Strategies for Active Flow Control using Graph Neural Networks](https://mlsanity.com/paper/2503.22775/) (2025)
- [Generalized Neural Operator for Parametric and Boundary-Value Problems](https://mlsanity.com/paper/2607.21932/) (2026)
- [FR3D: Three-dimensional Flow Reconstruction and Force Estimation for Unsteady Flows Around Extruded Bluff Bodies via Conformal Mapping Aided Convolutional Autoencoders](https://mlsanity.com/paper/2302.01802/) (2023)
- [Graph Neural Network-Informed Predictive Flows for Faster Ford-Fulkerson and PAC-Learnability](https://mlsanity.com/paper/2604.21175/) (2026)
- [Hybrid Lagrangian-Eulerian Model for Lagrangian Fluid Simulation](https://mlsanity.com/paper/2608.01164/) (2026)
- [VATO: A Vortex-Force-Aware Transformer Operator for Unsteady Separated Aerofoil Flows](https://mlsanity.com/paper/2609.00507/) (2026)

## Abstract (arXiv)

This paper introduces a novel neural network - flow completion network (FCN) - to infer the fluid dynamics, includ-ing the flow field and the force acting on the body, from the incomplete data based on Graph Convolution AttentionNetwork. The FCN is composed of several graph convolution layers and spatial attention layers. It is designed to inferthe velocity field and the vortex force contribution of the flow field when combined with the vortex force map (VFM)method. Compared with other neural networks adopted in fluid dynamics, the FCN is capable of dealing with bothstructured data and unstructured data. The performance of the proposed FCN is assessed by the computational fluiddynamics (CFD) data on the flow field around a circular cylinder. The force coefficients predicted by our model arevalidated against those obtained directly from CFD. Moreover, it is shown that our model effectively utilizes the exist-ing flow field information and the gradient information simultaneously, giving a better performance than the traditionalconvolution neural network (CNN)-based and deep neural network (DNN)-based models. Specifically, among all thecases of different Reynolds numbers and different proportions of the training dataset, the results show that the proposedFCN achieves a maximum norm mean square error of 5.86% in the test dataset, which is much lower than those of thetraditional CNN-based and DNN-based models (42.32% and 15.63% respectively).