Towards a unified data-driven turbulence model through multi-objective learning

  • Liu, Zhuoran (University of Stuttgart)
  • Wang, Haochen (University of Stuttgart)
  • Zhao, Zhuolin (University of Stuttgart)
  • Xiao, Heng (University of Stuttgart)

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Turbulence remains one of the last unresolved problems of classical physics and a major bottleneck to accurate flow prediction in climate, aerospace, and energy systems. Industrial simulations therefore rely on averaged representations of turbulence, which often struggle to predict flows governed by multiple interacting mechanisms. We present a unified, data-driven turbulence modeling framework designed to learn robustly from sparse, indirect observations across diverse flow regimes. The framework embeds physical consistency into a flexible, frame-invariant closure, selects representative training cases that cover diverse flow mechanisms based on flow-feature distribution similarity, and learns the model through a multi-objective ensemble strategy that balances competing objectives across flows and quantities of interest. The resulting unified foundation model, trained on multiple representative flows, adapts seamlessly across regimes without manual intervention. It outperforms existing turbulence models across a broad spectrum of canonical flows and maintains improved performance in realistic three-dimensional configurations of industrial relevance, including a generic car and a gas turbine diffuser. When application-specific accuracy is required, the framework further enables specialist models through additive fine-tuning on targeted flow datasets. These results demonstrate the feasibility of a deployable and generalized turbulence modeling approach that unifies multiple flow mechanisms within a single architecture for a broad range of natural and industrial flows.