标题： 基于扩散图网络学习复杂流体模拟的分布 显示英文标题

标题： Learning Distributions of Complex Fluid Simulations with Diffusion Graph Networks

摘要： 具有复杂非定常动力学的物理系统，如流体流动，通常很难通过单一平均解来准确表示。对于许多实际应用来说，访问可能状态的完整分布至关重要，从中可以推导出相关统计信息（例如，均方根和两点相关性）。在这里，我们提出了一种基于图的潜在扩散（或替代地，流匹配）模型，该模型在给定系统网格离散化及其物理参数的情况下，能够直接从其平衡分布中采样状态。这使得无需运行长时间且昂贵的数值模拟即可高效计算流动统计信息。基于图的结构使得能够在非结构化网格上进行操作，这对于用空间局部高梯度表示复杂几何结构至关重要，而使用多尺度GNN的潜在空间扩散建模则允许对整个解分布进行高效的学习和推理。一个关键发现是，即使在相对短的模拟数据上进行训练，所提出的网络也能准确学习完整的分布。我们将该方法应用于一系列流体力学任务，例如在湍流中预测三维机翼模型上的压力分布，在具有挑战性的场景中展示了其准确性和计算效率。直接采样准确解，并从较短的真实仿真中捕捉其多样性，对于复杂的科学建模任务具有高度前景。 显示英文摘要

摘要： Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which relevant statistics (e.g., RMS and two-point correlations) can be derived. Here, we propose a graph-based latent diffusion (or alternatively, flow-matching) model that enables direct sampling of states from their equilibrium distribution, given a mesh discretization of the system and its physical parameters. This allows for the efficient computation of flow statistics without running long and expensive numerical simulations. The graph-based structure enables operations on unstructured meshes, which is critical for representing complex geometries with spatially localized high gradients, while latent-space diffusion modeling with a multi-scale GNN allows for efficient learning and inference of entire distributions of solutions. A key finding is that the proposed networks can accurately learn full distributions even when trained on incomplete data from relatively short simulations. We apply this method to a range of fluid dynamics tasks, such as predicting pressure distributions on 3D wing models in turbulent flow, demonstrating both accuracy and computational efficiency in challenging scenarios. The ability to directly sample accurate solutions, and capturing their diversity from short ground-truth simulations, is highly promising for complex scientific modeling tasks.