发表机构
University of Alabama; University of Pittsburgh（阿拉巴马大学; 匹兹堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究人员推出TIDE三维湍流基准数据集，发现现有学习模型在该数据集上表现不佳，仅靠逐点误差无法保证物理保真度，需解决准确性、保真度和条件差距问题。
AI 中文摘要
湍流是物理动力学领域机器学习的核心测试平台，因为其控制定律是已知的精确形式。然而，现有大多数研究仍停留在二维层面，而三维湍流具有根本不同的物理特性，模拟成本也高得多。现有的三维资源通常每个配置仅提供一个实现，这使得难以区分是学习动力学还是拟合单一流动的统计特征。在本文中，我们推出TIDE（湍流不可压缩直接数值模拟集合），这是一个256³的直接数值模拟语料库和三维不可压缩湍流基准，包含八个受控轴上的15种配置、独立集合、压力场以及方程级验证。该基准包含五项任务、标准化的学习基线、受控泛化划分，以及逐点误差之外的物理保真度指标。在主要预测配置中，当前学习模型几乎未优于持续模型，在给定真实方程的情况下，其误差仍约为谱求解器的两倍。此外，较低的逐点误差可能伴随严重扭曲的小尺度动力学，表明仅靠准确性无法确保物理保真度。泛化结果进一步显示，多数状态转变反映了训练覆盖范围有限，而从受迫到衰减的迁移则暴露了一个缺失的条件变量：在受迫条件下训练的算子，在外部驱动移除后仍会预测受驱动的演化。缩小这些准确性、保真度和条件差距是TIDE可衡量的核心开放问题。
英文摘要
Turbulence is a central testbed for machine learning on physical dynamics because its governing laws are known exactly. However, most existing studies remain in 2D, while 3D turbulence has fundamentally different physics and is far more costly to simulate. Existing 3D resources also typically provide only one realization per configuration, making it difficult to distinguish learning the dynamics from fitting the statistics of a single flow. In this paper, we introduce TIDE (Turbulent Incompressible DNS Ensembles), a 256^3 DNS corpus and benchmark for 3D incompressible turbulence, with 15 configurations on eight controlled axes, independent ensembles, pressure fields, and equation-level verification. The benchmark includes five tasks, standardized learned baselines, controlled generalization splits, and physical-fidelity metrics alongside pointwise error. Across the main forecasting configurations, current learned models barely outperform persistence and still make about twice the error of a spectral solver given the true equations. Moreover, lower pointwise error can coincide with severely distorted small-scale dynamics, showing that accuracy alone does not ensure physical fidelity. Generalization results further show that most regime shifts reflect limited training coverage, whereas forced-to-decay transfer exposes a missing conditioning variable: operators trained under forcing continue to predict driven evolution when the external drive is removed. Closing these accuracy, fidelity, and conditioning gaps is the central open problem made measurable by TIDE.
Comments20 pages, 13 figures, 28 tables. Dataset: https://huggingface.co/datasets/ydai17/TIDE ; Code: https://github.com/Dyloong1/TIDE-dataset-benchmark ; DOI: https://doi.org/10.5281/zenodo.21589489
