Enhancing Graph U-Nets for Mesh-Agnostic Spatio-Temporal Flow Prediction

TL;DR

This work contributes to the field of reduced-order modeling for computational fluid dynamics by establishing Graph U-Nets as a viable and flexible alternative to convolutional neural networks, capable of accurately and efficiently predicting complex fluid flow phenomena across diverse scenarios.

Abstract

This study aims to overcome the limitations of conventional deep-learning approaches based on convolutional neural networks in complex geometries and unstructured meshes by exploring the potential of Graph U-Nets for unsteady flow-field prediction. We present a comprehensive investigation of Graph U-Nets, originally developed for classification tasks, now tailored for mesh-agnostic spatio-temporal forecasting of fluid dynamics. Our focus is on enhancing their performance through systematic hyperparameter tuning and architectural modifications. We propose novel approaches to improve mesh-agnostic spatio-temporal prediction of transient flow fields using Graph U-Nets, enabling accurate prediction on diverse mesh configurations. Key enhancements to the Graph U-Net architecture, including the Gaussian-mixture-model convolutional operator and noise injection approaches, provide increased flexibility in modeling node dynamics: the former reduces prediction error by 95\% compared to conventional convolutional operators, while the latter improves long-term prediction robustness, resulting in an error reduction of 86\%. We demonstrate the effectiveness of these enhancements in both transductive and inductive learning settings, showcasing the adaptability of Graph U-Nets to various flow conditions and mesh structures. This work contributes to the field of reduced-order modeling for computational fluid dynamics by establishing Graph U-Nets as a viable and flexible alternative to convolutional neural networks, capable of accurately and efficiently predicting complex fluid flow phenomena across diverse scenarios.

Figures (15)

• Figure 1: Graph U-Net architecture, where SC and PI denote skip-connection and pooling information respectively.
• Figure 2: Mesh used for training, containing 1,946 nodes, 11,208 edges, and 3,658 volume cells. The flow is from left to right and the details of the flow condition can be found in Table \ref{['tab:induct']} (named as baseline graph).
• Figure 3: Flowchart depicting how the rollout process is applied using the Graph U-Net: by using past $N$ snapshots as input, Graph U-Net predicts very next snapshot.
• Figure 4: Visualization of the $x$-velocity fields 50 snapshots after the trained snapshot range: iwGCN and GMM-1k operators are compared.
• Figure 5: Visualization of the $x$-velocity fields 100 snapshots after the trained snapshot range: predicted by the model with pooling ratio of 0.6 and model without pooling/unpooling operation.