Generative AI in Turbulence: Foundations, Applications, Validations and Benchmarks

Overview & Synopsis

Generative AI offers new approaches to turbulence problems in which incomplete observations or unresolved d.o.f. admit multiple physically plausible solutions. Potential applications include stochastic closures, super-resolution, data assimilation, uncertainty quantification, and the generation of Eulerian and Lagrangian flow ensembles. However, turbulence is not a conventional image-generation problem. Its multiscale dynamics, intermittency, extreme events, rough velocity fields and intrinsically stochastic transport make visual realism, pointwise error, and low-order spectral agreement insufficient measures of physical fidelity. We examine where generative AI provide novel capabilities with emphasis on diffusion models, score-based methods, and related probability-transport formulations. We discuss their use in unconditional generation, probabilistic reconstruction, reduced-order modeling, temporal evolution, and mesh-free representations. We argue that validation must address turbulence properties: energy transfer, structure functions, anomalous scaling, pdf tails, coherent structures, conservation laws, temporal consistency, ensemble diversity and generalization. Finally, we discuss potential limitations in validation, baseline, data availability and reproducibility, and the need for a benchmark ecosystem combining open data, standardized challenges, hidden tests, physics-aware metrics, and documented failures. This paper serves as a bridge between two communities. For AI practitioners, we provide a fair and accessible introduction to turbulence, essential for appreciating the challenges posed by the field and for assessing the physical relevance of generative models. For turbulent practitioners, we provide an introduction to the key technological aspects of Generative AI, clarifying what these tools actually do, and where their potential and current limitations lie.