Turbulence is nearly everywhere—from aircraft wings and gas-turbine blades to rivers, the
atmosphere, and the oceans—and predicting it accurately is central to reducing uncertainty in climate projections and to designing safer, more efficient aerospace and energy systems. Because fully resolving every scale of turbulence is prohibitively expensive in industrial simulations, engineers rely on Reynolds-averaged Navier—Stokes (RANS) solvers, which compute only the mean flow and delegate the averaged effect of turbulence to a turbulence model. The quality of that model largely determines the accuracy of the simulation.
For decades, however, turbulence models have been tuned for narrow classes of flow and lose accuracy outside them. The deeper difficulty is that different flow regimes impose conflicting requirements—an adjustment that improves one often degrades another. As the 2022 NASA Langley Turbulence Modeling Symposium concluded, after more than a decade of effort the community had yet to produce a data-driven model that surpasses existing ones in predictability, generality, and robustness.
In their NSR paper, the team reframes turbulence modeling as a multi-objective optimization problem. A physically consistent, frame-invariant neural-network representation of the turbulence closure is paired with an automatic, distribution-distance-based method that selects nine representative flows from a library of 36 canonical-to-complex cases. Training then seeks a Pareto-optimal balance among competing objectives arising from different flows and quantities of interest, reconciling their conflicts within a single model.
Trained on just nine flows, the unified foundation model was tested on 27 unseen cases—spanning attached boundary layers, free-shear, secondary, and separated flows—and matched or outperformed the baseline in nearly all of them. It also improved predictions for complex three-dimensional configurations, including a generic car, a three-dimensional diffuser, and a generic aircraft. When higher accuracy is needed for a specific application, a compact “additive fine-tuning” step converts the unified foundation model into a specialist, sharply improving, for instance, the separation prediction in a challenging three-dimensional diffuser.
“For decades, the field has tried to build a turbulence model that works everywhere, but
improving one type of flow usually spoils another,” said Heng Xiao, professor at the University of Stuttgart and the study's corresponding author. “By treating these competing demands as a multi-objective optimization, we can train a single model to handle many flow mechanisms at once, without manual intervention—making the approach both more general and more practical for real industrial simulations.”
Beyond the cases studied here, the authors note that the framework scales to many more
objectives, pointing toward unified models for entire devices—such as a complete gas turbine or aircraft—rather than isolated flow regions. More broadly, the study illustrates how machine learning can reconcile competing physical demands within a single model, offering a practical path toward deployable, generalizable turbulence models.
The study was conducted by PhD students Zhuoran Liu, Haochen Wang, and Zhuolin Zhao at the University of Stuttgart. Zhuoran Liu led the research as first author, and Professor Heng Xiao served as the corresponding author.
National Science Review
Computational simulation/modeling