用图神经网络融合物理规律，从稀疏数据重建三维流体冲击波。
A Physics-Augmented GraphGPS Framework for the Reconstruction of 3D Riemann Problems from Sparse Data
- 基于图结构的消息传递与位置编码，融合物理约束进行流场重建。
- 在稀疏观测下重建冲击波和间断面效果更清晰，计算效率更高。
- 适合做高保真流体模拟或科学计算的工程师与研究人员。
在可压缩流体中，从稀疏测量数据重构激波、间断、膨胀波及其相互作用是一个重要的逆问题，具有广泛的实际应用价值。近年来，物理信息机器学习成为解决此类重建任务的热门方法。本文探索了一种名为 GraphGPS 的机器学习框架，用于从稀疏观测中物理感知地重建经典的三维黎曼问题（3D Riemann problems）。该框架结合了位置编码、图的局部消息传递与全局上下文感知能力，并通过消融实验验证了后两者的重要性。我们改进了消息传递的聚合步骤，使其能感知激波与间断面，从而获得更锐利的特征重建。此外，我们设计消息传递仅从已知节点传播信息，实现了计算量降低、训练收敛更快，且重建精度无下降。实验表明，GraphGPS 在多个机器学习基准上均优于现有方法。
原文摘要 · Abstract (English)
In compressible fluid flow, reconstructing shocks, discontinuities, rarefactions, and their interactions from sparse measurements is an important inverse problem with practical applications. Moreover, physics-informed machine learning has recently become an increasingly popular approach for performing reconstructions tasks. In this work we explore a machine learning recipe, known as GraphGPS, for reconstructing canonical compressible flows known as 3D Riemann problems from sparse observations, in a physics-informed manner. The GraphGPS framework combines the benefits of positional encodings, local message-passing of graphs, and global contextual awareness, and we explore the latter two components through an ablation study. Furthermore, we modify the aggregation step of message-passing such that it is aware of shocks and discontinuities, resulting in sharper reconstructions of these features. Additionally, we modify message-passing such that information flows strictly from known nodes only, which results in computational savings, better training convergence, and no degradation of reconstruction accuracy. We also show that the GraphGPS framework outperforms numerous machine learning benchmarks.
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