Integration of Temporal Dynamics in Graph U-Nets for Improved Mesh-Agnostic Spatio-Temporal Flow Prediction*

This study addresses the limitations of conventional deep-learning approaches based on convolutional neural networks, particularly their dependency on structured meshes, which restricts their applicability to complex geometries and unstructured meshes. Building on previous advancements in mesh-agnostic spatio-temporal prediction of transient flow fields using graph U-Nets, this work proposes further refinements by integrating temporal schemes commonly used in computational fluid dynamics (CFD). These enhancements aim to harmonize the machine learning framework with the physical principles of flow physics. Key objectives include improving accuracy and robustness in spatio-temporal flow predictions across diverse mesh configurations through the incorporation of temporal dynamics. The research will explore the effects of different temporal schemes on graph U-Net performance, identifying optimal configurations for enhanced predictive capabilities. The study will also investigate the impact of these enhancements on both transductive and inductive learning settings, aiming to accurately predict quantities for unseen nodes within trained graphs and generalize performance to new mesh configurations with varying flow conditions. This work aims to develop advanced graph U-Net models that integrate CFD temporal schemes, enhancing their applicability and reliability in real-world engineering applications involving complex fluid dynamics.