[论文] FlowReconBench: Accuracy, calibration and cost of learned and classica...

论文概要

研究领域: ML 作者: Nicolas Tricard, Linzheng Wang, Jason Chen, Sili Deng 发布时间: 2026-11-04 arXiv: 2611.06912

中文摘要

从稀疏传感器重建完整流场需要对未测量区域和物理变量做出先验假设。然而学习模型何时优于经典估计器、以及它们预测的哪些方面可信，仍不清楚。FlowReconBench 在三种流动形态下评估 10 种学习方法和 5 种经典方法：跨雷诺数的层流圆柱尾迹、二维 Kolmogorov 湍流和大尺度三维各向同性湍流。所有方法共享防泄漏的数据划分和传感器采样，在逐通道误差、集合离散度、校准性、能谱和成本上评分。领先方法随场景而变：经典方法在低阶和密集感知场景表现强劲——圆柱尾迹上线性随机估计和 gappy POD 领先（含未观测压力）；3D 场景中反距离加权在已观测通道上媲美最佳学习方法。数据驱动方法在传感器密度降低或可观测性变差时更优。Kolmogorov 流上 CRPS 与误差给出不同排序：生成模型集合更宽但欠分散，确定性模型优先逐点误差。生成模型通过采样器预算平衡此权衡——更大预算以更高计算代价改善集合质量。3D 扩展测试表明可查询方法内存开销平坦，而全网格构建方法内存溢出。仅观测 4 场中的 2 场使问题运动学欠约束，但潜变量模型仍能复现与真值的结构相似性。

原文摘要

Reconstructing full flow fields from sparse sensors requires prior assumptions about unmeasured regions and physical variables. Yet it remains unclear when learned models outperform classical estimators and which aspects of their predictions can be trusted. FlowReconBench evaluates ten learned and five classical methods on three regimes: a laminar cylinder wake across Reynolds numbers, two-dimensional Kolmogorov turbulence and a large-scale three-dimensional (3D) isotropic turbulence. Methods share leakage-controlled splits and sensor draws and are scored on per-channel error, ensemble spread, calibration, spectra and cost. The leading method changes for each regime. Classical methods perform strongly in low-order and dense-sensing regimes. On the cylinder wake, linear stochastic estimatio...

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