提出RWR模型融合全局与局部处理,提升复杂仿真精度与效率
Read, Write, Relax: Why Neural PDE Surrogates Need Both Global and Local Processing

- 将注意力机制与消息传递交替使用,统一建模全局与局部信息
- 在工业级大规模网格上误差显著降低,优于现有主流方法
- 适合数据稀缺场景,对工程关键量预测准确且可扩展至大规模问题
近期基于网格的仿真进展很大程度依赖两类神经代理:一类是通过少量隐状态令牌进行全局信息传播的全局模型,另一类是在网格边上传播消息的局部模型。但两者均难以应对高维或大规模、复杂的实际工业问题。本文揭示其根本局限:全局注意力如空间低通滤波器,而局部消息传递缺乏全局覆盖能力。从误差角度看,两类操作恰为多网格循环的两半——分别校正谱的低频与高频误差,无法互代。为此提出读-写-松弛(Read-Write-Relax, RWR)框架,将隐状态注意力与消息传递松弛交替整合于统一架构中。该设计实现全频谱误差降低,在多个工业与公开基准测试中几乎全面领先。同时在数据稀缺条件下表现优异,精准预测工程关注量,并成功拓展至挑战性大规模全场仿真任务。
原文摘要 · Abstract (English)
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.
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