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

TL;DR

This paper enhances Graph U-Nets for mesh-agnostic spatio-temporal flow prediction, achieving significant accuracy improvements through architectural innovations, making them a promising tool for complex fluid dynamics modeling.

Contribution

It introduces novel modifications to Graph U-Nets, including Gaussian-mixture-model convolution and noise injection, to improve mesh-agnostic flow prediction accuracy and robustness.

Findings

Reduced prediction error by 95% with Gaussian-mixture convolution

Improved long-term prediction robustness by 86% with noise injection

Effective in both transductive and inductive learning settings

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.