AutoTurb: Using large language models for automatic algebraic turbulence model discovery

Symbolic regression (SR) methods have been extensively investigated to explore explicit algebraic Reynolds stress models (EARSM) for turbulence closure of Reynolds-averaged Navier-Stokes (RANS) equations. The deduced EARSM can be readily implemented in existing computational fluid dynamic (CFD) codes and promotes the identification of physically interpretable turbulence models. Recently, large language models (LLMs) trained on large amounts of publicly available source code have drawn great attention for their abilities to automatically discover equations with more general free-text inputs and problem descriptions and provide wider possibilities with novel insights. This work proposes a novel framework, named “AutoTurb,” using LLMs to automatically discover algebraic expressions for correcting the linear Reynolds stress model. The direct Reynolds stress and the indirect RANS output (e.g., velocity field) are both involved in the training objective to guarantee data consistency and avoid numerical stiffness. An evolutionary search framework is used for global optimization, where constraints on functional complexity and simulation convergence are integrated into the objective to manage the extensive flexibility of LLMs. The proposed method is performed for separated flow over periodic hills. The generalizability of the discovered model is verified on a set of 2D turbulent separated flows with different Reynolds numbers and geometries. Results show that the corrected RANS enhances predictions of both Reynolds stress and mean velocity fields. Compared to models from other studies, our discovered model shows superior accuracy and generalization capability. The proposed approach provides a promising paradigm for using LLMs to improve turbulence modeling for a given class of flows. © 2025 Author(s)