# Learning Effective Dynamics across Spatio-Temporal Scales of Complex Flows

arXiv: https://arxiv.org/abs/2502.07990 · HTML: https://mlsanity.com/paper/2502.07990/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 55 references that are in the map.
- First posted on arXiv 11 Feb 2025.

## Builds on (most cited first, 28 of 28)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [PointNet++: Deep Hierarchical Feature Learning on Point Sets in a Metric Space](https://mlsanity.com/paper/1706.02413/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Learning to Simulate Complex Physics with Graph Networks](https://mlsanity.com/paper/2002.09405/) (2020)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Rethinking FID: Towards a Better Evaluation Metric for Image Generation](https://mlsanity.com/paper/2401.09603/) (2023)
- [Graph networks as learnable physics engines for inference and control](https://mlsanity.com/paper/1806.01242/) (2018)
- [Professor Forcing: A New Algorithm for Training Recurrent Networks](https://mlsanity.com/paper/1610.09038/) (2016)
- [Data-Driven Forecasting of High-Dimensional Chaotic Systems with Long Short-Term Memory Networks](https://mlsanity.com/paper/1802.07486/) (2018)
- [Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive Networks](https://mlsanity.com/paper/1906.05747/) (2019)
- [Transformers for Modeling Physical Systems](https://mlsanity.com/paper/2010.03957/) (2020)
- [PhyCRNet: Physics-informed Convolutional-Recurrent Network for Solving Spatiotemporal PDEs](https://mlsanity.com/paper/2106.14103/) (2021)
- [Learned Coarse Models for Efficient Turbulence Simulation](https://mlsanity.com/paper/2112.15275/) (2021)
- [Multiscale Simulations of Complex Systems by Learning their Effective Dynamics](https://mlsanity.com/paper/2006.13431/) (2020)
- [POD-DL-ROM: enhancing deep learning-based reduced order models for nonlinear parametrized PDEs by proper orthogonal decomposition](https://mlsanity.com/paper/2101.11845/) (2021)
- [Multi-level Convolutional Autoencoder Networks for Parametric Prediction of Spatio-temporal Dynamics](https://mlsanity.com/paper/1912.11114/) (2019)
- [Graph Element Networks: adaptive, structured computation and memory](https://mlsanity.com/paper/1904.09019/) (2019)
- [Physical Design using Differentiable Learned Simulators](https://mlsanity.com/paper/2202.00728/) (2022)
- [Deep Neural Networks for Nonlinear Model Order Reduction of Unsteady Flows](https://mlsanity.com/paper/2007.00936/) (2020)
- [Multi-fidelity Generative Deep Learning Turbulent Flows](https://mlsanity.com/paper/2006.04731/) (2020)
- [Conditionally Parameterized, Discretization-Aware Neural Networks for Mesh-Based Modeling of Physical Systems](https://mlsanity.com/paper/2109.09510/) (2021)
- [Eigen-GNN: A Graph Structure Preserving Plug-in for GNNs](https://mlsanity.com/paper/2006.04330/) (2020)
- [Interpretable A-posteriori Error Indication for Graph Neural Network Surrogate Models](https://mlsanity.com/paper/2311.07548/) (2023)
- [Nonlinear embeddings for conserving Hamiltonians and other quantities with Neural Galerkin schemes](https://mlsanity.com/paper/2310.07485/) (2023)
- [GNUMAP: A Parameter-Free Approach to Unsupervised Dimensionality Reduction via Graph Neural Networks](https://mlsanity.com/paper/2407.21236/) (2024)
- [Scalable and Consistent Graph Neural Networks for Distributed Mesh-based Data-driven Modeling](https://mlsanity.com/paper/2410.01657/) (2024)

## Built on by (most cited first, 2 of 2)

- [Generative Urban Flow Modeling: From Geometry to Airflow with Graph Diffusion](https://mlsanity.com/paper/2512.14725/) (2025)
- [A Mechanistic Analysis of Transformers for Dynamical Systems](https://mlsanity.com/paper/2512.21113/) (2025)

## Abstract (arXiv)

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.