Learning Effective Dynamics across Spatio-Temporal Scales of Complex Flows

2025-02-11

AI Summary

Addressing the challenge of modeling dynamic cross-scale spatiotemporal interactions in multiscale complex fluid dynamics, this paper proposes Graph-LED—a novel framework coupling graph neural networks (GNNs) with autoregressive attention mechanisms. It innovatively encodes unstructured-grid flow fields as dynamic graphs, synergistically leveraging GNNs’ spatial dimensionality reduction and attention mechanisms’ temporal modeling capability to enable efficient multiscale dynamical learning on variable-resolution meshes. The method requires only limited simulation data to capture cross-scale coupling relationships. Evaluated on canonical benchmarks—including flow past a circular cylinder and backward-facing step flow—Graph-LED accurately reproduces near-wall fine-scale structures and far-field wake evolution, significantly outperforming conventional reduced-order models. This work establishes a scalable, data-efficient modeling paradigm for complex flows where full-scale direct numerical simulation remains computationally intractable.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Intelligent Robots: Multimodal Perception & Sensor Fusion

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Multilingual and cross-lingual Web search

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.

Problem

• Modeling complex fluid flows
• Learning cross-scale dynamics
• Forecasting spatio-temporal physics

Innovation

• Graph neural networks
• Attention-based autoregressive model
• Unstructured meshes dimensionality reduction