arXiv:2607.23667math.NAcs.LG2026-07

不同流动场景下,同一类代理模型表现差异大,选型需匹配流动动力学特征。

No Free Lunch in Flow Surrogates under Time-Varying Boundary Conditions: A Two-Regime Study

论文配图:No Free Lunch in Flow Surrogates under Time-Varying Boundary Conditions: A Two-Regime Study
图 1 · 摘自论文原文
  • 按全场或隐空间学习,一次性或逐步预测,不同场景各有优劣
  • 薄膜流中模型误差仅3.2%,涡街流中保留96%脱落能量
  • 评估应关注物理特性而非单一误差,适合仿真加速与工业应用

在模拟半导体制造中化学机械平坦化(CMP)的三维浆料膜和圆柱后方二维卡门涡街(KVS)两种瞬态流动中,比较八种代理模型在时间变化边界条件下的表现。模型分两类:学习全场或隐空间表示,预测方式为一步到位或逐步递推。无单一架构在两场景均胜出。薄膜流中,一次性全场模型对累积壁面剪切应力重建误差仅3.2%;涡街流中,基于隐空间的自回归DeepONet保留96%脱落能量,而直接和一步模型几乎衰减至零。关键区别在于时间处理方式:自回归反馈提供相位记忆,适合自持涡街;直接映射则更适于边界驱动的薄膜。点对点均方根误差在两场景均误导选择,因此改用五个物理问题评估:场分布、结构、虚构运动、振幅与时间。训练后的代理模型比有限元求解器快1000至10000倍,但训练成本意味着对于CMP从第一个查询起即有收益,对于KVS则需第三个查询后才回本。模型选择应基于目标流动的动力学特性,验证也需使用故障模式分辨指标,因为最优架构及其验证均不具泛化性。

原文摘要 · Abstract (English)

A flow surrogate validated on a simple regime is often taken as evidence that the approach will carry to a richer one. We test this assumption on two transient flows under time-varying boundary conditions emulating the process startup: the three-dimensional slurry film in chemical-mechanical planarisation (CMP), a core semiconductor-manufacturing process, and the two-dimensional Karman vortex street (KVS) behind a cylinder. Eight surrogate models are compared on one shared evaluation pipeline, differing in whether they learn the full field or a latent representation, and whether they predict trajectories in one shot or step by step. No single architecture wins both regimes. On the film, a one-shot full-field model reconstructs the process-relevant cumulative wall shear stress to 3.2% relative error. On the wake, a latent autoregressive DeepONet retains 96% of the shedding power that direct and one-shot models damp to almost zero. The deciding axis is the treatment of time. The self-sustained wake requires the phase memory that autoregressive feedback provides, while the boundary-driven film rewards a direct map. Pointwise RMSE picks the wrong model in both regimes, so the evaluation scores five physical questions instead, the field, its structure, invented motion, amplitude, and timing. The trained surrogates answer queries $10^3$ to $10^4$ times faster than the finite-element solver, but the offline cost of the training simulations means they pay off from the first query beyond the training set for CMP and the third for the KVS. The choice of surrogate should follow the dynamical character of the target flow, and its validation should use failure-mode-resolved metrics, since neither the winning architecture nor its validation transfers.

流动代理动态边界模型选择物理评估

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