Symbolic turbulence model development for complex-geometry flows exploiting language model-based transfer learning

Evolutionary symbolic regression methods, such as Genetic Programing or Gene Expression Programing (GEP), enable the exploration of turbulence models for Reynolds-averaged Navier–Stokes (RANS) simulations. However, these models often encounter limitations when addressing phenomena beyond their training distribution. While expanding the number of training cases or extending the exploration time could mitigate these issues, the required increase in computational budget restricts such approaches, especially when considering engineering-relevant scenarios. Conversely, knowledge from prior optimizations might be available, but initial candidate solutions are typically generated randomly and rarely incorporate preliminary assumptions to limit the search space. In contrast, transfer learning, widely used for neural networks, offers a solution by reusing knowledge from pre-trained models, but its application to symbolic regression for turbulence modeling remains unexplored. This study introduces a novel framework leveraging the transfer learning methodology for the GEP to develop turbulence closures for RANS. The framework integrates a language model, parameterized without necessitating significant resources, to discern recurring patterns within equations obtained from previous optimizations. The performance is demonstrated on a three-dimensional, highly bent duct, including various physical phenomena. The language model is pre-trained based on simpler building-block flows exhibiting some phenomena present in the highly bent duct, i.e., a canonical duct flow featuring secondary flows and the case of the periodic hill displaying flow separation and reattachment. It is demonstrated that a more targeted and efficient model exploration can be achieved by augmenting the initial set of candidate solutions using a language model and superimposing model information from distinct prior optimizations.