Machine‐Learning Enhanced Parametric Reynolds‐Averaged Navier‐Stokes Equations at the Full‐ and Reduced‐Order Levels

In this contribution, we focus on the Reynolds‐averaged Navier‐Stokes (RANS) models and their exploitation to build reliable reduced‐order models to further accelerate predictions for real‐time applications and many‐query scenarios. Specifically, we investigate how machine learning can be employed to enhance the predictive capabilities of the model, both at the full‐order model (FOM) and reduced‐order model (ROM) levels. We explore a novel integration of these two areas. We generate the FOM snapshots, essential for ROM construction, using a data‐driven RANS model: the ‐Vector Basis Neural Network. This is the first time that this machine‐learning procedure covers a large parametric variation, and we propose tailored training strategies to increase the accuracy of the FOM model. At the ROM level, we compare the results obtained by standard proper orthogonal decomposition (POD) in an intrusive Galerkin setting (PODG) and POD neural network approach (PODNN). The numerical validation is conducted on a classic turbulent square‐duct flow benchmark, with the bulk Reynolds number as the sole varying parameter. Our investigation reveals that the PODG method proves to be unstable and inaccurate for turbulent flow prediction, while PODNN demonstrates superior performance in terms of accuracy and computational efficiency.