Estimating fluid dynamics is classically done through the simulation and integration of numerical models solving the Navier-Stokes equations, which is computationally complex and time-consuming even on high-end hardware. This is a notoriously hard problem to solve, which has recently been addressed with machine learning, in particular graph neural networks (GNN) and variants trained and evaluated on datasets of static objects in static scenes with fixed geometry. We attempt to go beyond existing work in complexity and introduce a new model, method and benchmark. We propose EAGLE, a large-scale dataset of 1.1 million 2D meshes resulting from simulations of unsteady fluid dynamics caused by a moving flow source interacting with nonlinear scene structure, comprised of 600 different scenes of three different types. To perform future forecasting of pressure and velocity on the challenging EAGLE dataset, we introduce a new mesh transformer. It leverages node clustering, graph pooling and global attention to learn long-range dependencies between spatially distant data points without needing a large number of iterations, as existing GNN methods do. We show that our transformer outperforms state-of-the-art performance on, both, existing synthetic and real datasets and on EAGLE. Finally, we highlight that our approach learns to attend to airflow, integrating complex information in a single iteration.

翻译：摘要：流体动力学的估算通常通过求解纳维-斯托克斯方程的数值模型进行模拟与积分，即便在高端硬件上，这一过程仍存在计算复杂且耗时的难题。该问题历来极具挑战性，近期被机器学习方法所探索，特别是图神经网络（GNN）及其变体，它们基于固定几何形状的静态场景中静态物体的数据集进行训练与评估。我们尝试超越现有研究在复杂性上的局限，提出新的模型、方法与基准。我们构建EAGLE数据集——包含因移动流源与非线性场景结构相互作用引发的非稳态流体动力学模拟产生的110万个二维网格，涵盖600个不同场景（分属三种类型）。为在具有挑战性的EAGLE数据集上实现压力与速度的未来预测，我们引入一种新型网格变换器。该模型通过节点聚类、图池化与全局注意力机制，在无需大量迭代（现有GNN方法所需）的条件下，学习空间远端数据点之间的长程依赖关系。实验表明，我们的变换器在现有合成与真实数据集以及EAGLE上均优于当前最优性能。最后，我们强调该方法通过单次迭代整合复杂信息，学会关注气流特征。