Large language model driven development of turbulence models

Artificial intelligence (AI) has achieved human-level performance in specialised tasks such as Go, image recognition and protein folding, raising the prospect of an AI singularity – where machines not only match, but surpass human reasoning. Here, we demonstrate a step towards this vision in the context of turbulence modelling. By treating a large language model (LLM), DeepSeek-R1, as an equal partner, we establish a closed-loop, iterative workflow in which the LLM proposes, refines and reasons about near-wall turbulence models under adverse pressure gradients (APGs), system rotation and surface roughness. Through multiple rounds of interaction involving long-chain reasoning and a priori and a posteriori evaluations, the LLM generates models that not only rediscover established strategies, but also synthesise new ones that outperform baseline wall models. Specifically, it recommends incorporating a material derivative to capture history effects in APG flows, modifying the law of the wall to account for system rotation and developing rough-wall models informed by surface statistics. In contrast to conventional data-driven turbulence modelling – often characterised by human-designed, black-box architectures – the models developed here are physically interpretable and grounded in clear reasoning.