A transfer learning approach for data-driven turbulence modeling

The Reynolds-Averaged Navier-Stokes (RANS) equations are widely used to predict engineering flow fields, but traditional Reynolds stress closure models lead to only partially reliable predictions. Recently, with continuing advances in high performance computing and machine learning practices, data-driven turbulence modeling is becoming possible. In this work, the Reynolds stress anisotropy tensor is learned using a physics-aware machine learning model. The Tensor Basis Neural Network (TBNN), first proposed by Ling et al., is tested on turbulent channel flow at various Reynolds numbers.  Numerical experiments demonstrate that the TBNN is fundamentally limited by the mathematical structure of the underlying tensor basis.  In spite of this limitation, the neural network makes an effort to match the provided turbulence data by adjusting model parameters.  With these observations in mind, the TBNN model is trained on turbulent channel flow data at several Reynolds numbers and used to predict the Reynolds stress tensor at a different Reynolds number.  We show that adjustments to the neural network architecture via transfer learning techniques improve predictions of the Reynolds stress tensor.