arXiv:2608.04222 · v2
TIDE: A Physically Diverse 3D Turbulence Benchmark Dataset for Advancing Scientific Machine Learning
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 trained under a fixed reference recipe 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. Rollout stability depends on the configuration, the training seed, and how densely training samples each trajectory. Joint training across neighboring regimes does not close the transfer gaps we test, and the forced-to-decay contrast bounds a conditioning limit: an estimate of the current forcing state removes 20-41% of the error a spectral solver makes without forcing input, while history or forcing inputs help only some learned architectures. Closing these accuracy, fidelity, and conditioning gaps is the central open problem made measurable by TIDE. https://github.com/Dyloong1/TIDE-dataset-benchmark
作者备注：20 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