Interpreting tensor basis neural networks with symbolic transcendental Reynolds stress models for transonic axial compressor flows

Transonic axial compressor flows exhibit complex turbulence structures that pose significant challenges for traditional turbulence models. In recent years, neural network-based turbulence models have demonstrated promising results in simulating these intricate flows. However, these models often lack interpretability, a crucial aspect of understanding the underlying physical mechanisms. Symbolic regression, capable of training highly interpretable turbulence models, offers a potential solution to elucidate the mechanisms underpinning neural network-based turbulence models. In this study, we employ evolutionary symbolic regression to interpret tensor basis neural networks (TBNNs) and develop explicit transcendental Reynolds stress models (ETRSM) for transonic axial compressor flows. Our symbolic regression turbulence models are trained on the inputs and outputs of a pre-trained TBNN. We introduce a method that independently predicts coefficients for each tensor basis, significantly reducing computational costs and enhancing the rationality of the prediction process. We develop six symbolic regression models: three transcendental and three algebraic. Through rigorous computational fluid dynamics (CFD) simulations, the transcendental models demonstrate an exceptional ability to interpret the TBNN, while the algebraic models show limited success. The symbolic regression ETRSM, characterized by high interpretability and transferability, effectively interprets the pre-trained TBNN and achieves comparable accuracy to TBNN-based turbulence models in simulating the complex turbulence flows in transonic axial compressors. These results underscore the potential of symbolic regression turbulence models for simulating industry-level CFD problems and highlight the importance of incorporating additional features in training such models. Furthermore, the method separates the prediction of individual tensor basis coefficients, significantly reducing computational costs.