Learning Effective Dynamics across Spatio-Temporal Scales of Complex Flows

TL;DR

This paper introduces Graph-LED, a novel framework using graph neural networks and attention models to effectively learn and forecast complex fluid dynamics across multiple spatio-temporal scales from limited data.

Contribution

The work presents a new graph-based learning framework that captures multi-scale fluid flow dynamics using GNNs and autoregressive attention, handling unstructured meshes and complex geometries.

Findings

Accurately predicts flow past a cylinder and wake effects.

Robust forecasting across different Reynolds numbers.

Effectively captures small-scale and large-scale flow features.

Abstract

Modeling and simulation of complex fluid flows with dynamics that span multiple spatio-temporal scales is a fundamental challenge in many scientific and engineering domains. Full-scale resolving simulations for systems such as highly turbulent flows are not feasible in the foreseeable future, and reduced-order models must capture dynamics that involve interactions across scales. In the present work, we propose a novel framework, Graph-based Learning of Effective Dynamics (Graph-LED), that leverages graph neural networks (GNNs), as well as an attention-based autoregressive model, to extract the effective dynamics from a small amount of simulation data. GNNs represent flow fields on unstructured meshes as graphs and effectively handle complex geometries and non-uniform grids. The proposed method combines a GNN based, dimensionality reduction for variable-size unstructured meshes with an autoregressive temporal attention model that can learn temporal dependencies automatically. We evaluated the proposed approach on a suite of fluid dynamics problems, including flow past a cylinder and flow over a backward-facing step over a range of Reynolds numbers. The results demonstrate robust and effective forecasting of spatio-temporal physics; in the case of the flow past a cylinder, both small-scale effects that occur close to the cylinder as well as its wake are accurately captured.