时变边界条件下流动代理模型的无免费午餐定理：双工况研究
No Free Lunch in Flow Surrogates under Time-Varying Boundary Conditions: A Two-Regime Study
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中文总结 AI 辅助
研究时变边界条件下CMP三维浆料膜流动和KVS二维卡门涡街流动，比较八个代理模型，发现无单一架构在两种工况均优，选择代理应依目标流动动力学特性，训练后模型回答查询比有限元求解器快，验证要用故障模式解析指标。
中文摘要 AI 辅助
在简单工况下验证的流动代理模型通常被视为其可推广到更复杂工况的证据。本文通过模拟过程启动的时变边界条件下的两个瞬态流动来检验这一假设，即化学机械平面化（CMP）中的三维浆料膜流动和圆柱后二维卡门涡街（KVS）流动。在一个共享评估管道上比较了八个代理模型，它们在是否学习全场或潜在表示以及是一次性预测轨迹还是逐步预测轨迹方面存在差异。没有单一架构能在两种工况下都获胜。在浆料膜流动中，一次性全场模型将与工艺相关的累积壁面剪应力重构到3.2%的相对误差。在尾流中，潜在自回归深度算子网络（DeepONet）保留了96%的脱落功率，而直接和一次性模型几乎将其衰减至零。决定性因素是对时间的处理。自持尾流需要自回归反馈提供的相位记忆，而边界驱动的浆料膜流动则受益于直接映射。逐点均方根误差（RMSE）在两种工况下都选错了模型，因此评估采用了五个物理问题，即场、其结构、虚构运动、振幅和时间。训练后的代理模型比有限元求解器快10³到10⁴倍回答查询，但训练模拟的离线成本意味着它们在CMP的训练集之外的第一个查询以及KVS的第三个查询之后才开始有回报。代理模型的选择应遵循目标流动的动力学特性，其验证应使用故障模式解析指标，因为获胜架构及其验证都不能转移。
英文摘要
We test whether an architecture that succeeds on a simple flow regime also succeeds on a richer one, with each trained separately on each regime. We explore two transient flows under time-varying boundary conditions: the three-dimensional slurry film in chemical-mechanical planarisation (CMP), central to semiconductor manufacturing, and the two-dimensional Kármán vortex street (KVS). Eight surrogate models on one shared pipeline differ in whether they learn the full field or a latent representation, and in whether they predict in one shot or step by step. No single architecture wins both regimes. On the film, a one-shot full-field model reconstructs the cumulative wall shear stress to 2.7% relative error. On the wake, a latent autoregressive DeepONet retains 90% of the shedding power that direct and one-shot models damp to almost zero. The treatment of time decides the outcome. The self-sustained wake calls for autoregressive feedback and the boundary-driven film for a direct map. Pointwise RMSE hides the damped oscillation on the wake, compresses the sixfold lead on the film's process target, and picks the damped model under wake extrapolation. The evaluation scores five physical questions. Trained surrogates answer queries 10^3 to 10^4 times faster than the finite-element solver and pay off from the first query beyond the training set on the film and from the third on the wake. Neither the winning architecture nor its validation holds across regimes. The choice of surrogate should follow the dynamical character of the target flow, and its validation should resolve the failure modes.
发表机构
- Chemnitz University of Technology（开姆尼茨工业大学）
机构由 AI 辅助整理，请以论文原文为准。
