Learning Effective Dynamics across Spatio-Temporal Scales of Complex Flows

• URL: http://arxiv.org/abs/2502.07990v1
• Date: Tue, 11 Feb 2025 22:14:30 GMT
• Title: Learning Effective Dynamics across Spatio-Temporal Scales of Complex Flows
• Authors: Han Gao, Sebastian Kaltenbach, Petros Koumoutsakos,
• Abstract summary: We propose a novel framework, Graph-based Learning of Effective Dynamics (Graph-LED), that leverages graph neural networks (GNNs) and an attention-based autoregressive model. We evaluate 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.
• Score: 4.798951413107239
• License:
• 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.

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