AI 中文总结
针对工业模拟中神经PDE代理无法处理复杂网格的问题，提出RWR模型，通过交织潜在注意力与消息传递松弛，在基准测试中精度最高且数据效率优，可处理大规模问题。
AI 中文摘要
近期基于网格的模拟进展在很大程度上依赖于两类不同的神经代理：通过少量潜在令牌传递信息的全局模型，以及在网格边缘执行消息传递的局部模型。这两类模型均无法处理低维问题、小尺度或过于简化的网格之外的场景，而工业问题正属于这些模拟场景。我们的工作明确展示了这一点，并提出了统一的公式。在全局方法中，潜在令牌注意力充当空间低通滤波器，而局部消息传递缺乏在大网格空间中传播信息所需的全局范围。从误差角度看，这两个算子是多重网格循环的两半：一个校正频谱低端的误差，另一个校正频谱高端的误差，二者均无法完成对方的工作。我们引入了Read-Write-Relax（RWR），其在统一公式下将潜在注意力与消息传递松弛交织在一起。这种交织处理器可降低整个频谱的误差，使RWR在我们的工业和公共基准的几乎所有比较中成为最准确的模型。它在数据稀缺场景中也具有显著的数据效率，对工程关注量准确，且能将全场预测扩展到具有挑战性的大规模问题。
英文摘要
Recent mesh-based simulation advances have, in no small part, relied on neural surrogates of two distinct families: global models that route information through a small set of latent tokens, and local models that perform message passing across mesh edges. Consistent with both classes is the inability to perform beyond low-dimensional problems and small-scale or oversimplified meshes, the simulation regimes where industrial problems reside. Our work shows this explicitly and presents a unified formulation. In global approaches, latent-token attention acts as a spatial low-pass filter, while local message passing lacks the global reach necessary to propagate information across large mesh spaces. Viewed through the error, the two operators are the halves of a multigrid cycle: one corrects errors at the lower end of the spectrum, the other at the higher end, and neither can do the other's job. We introduce Read-Write-Relax (RWR), which interleaves latent attention with message-passing relaxation under a unified formulation. The interleaved processor lowers error across the entire spectrum, making RWR the most accurate model in nearly every comparison across our industrial and public benchmarks. It is also markedly data-efficient in the scarce-data regimes, accurate on the engineering quantities of interest, and scales full-field predictions to challenging, large-scale problems.
Comments26 pages, 14 figures
