Soufiane Cherroud | Searcharxiv

arXiv2025

Machine-learning-assisted Blending of Data-Driven Turbulence Models

We present a machine learning-based framework for blending data-driven turbulent closures in the Reynolds-Averaged Navier-Stokes (RANS) equations, aimed at improving their generalizability across diverse flow regimes. Specialized models (hereafter referred to as experts) are trained via sparse Bayesian learning and symbolic regression for distinct flow classes, including turbulent channel flows, separated flows, and a near-sonic axisymmetric jet. These experts are then combined intrusively within the RANS equations using weighting functions, initially derived via a Gaussian kernel on a dataset spanning equilibrium shear conditions to separated flows. Finally, a Random Forest Regressor is trained to map local physical features to these weighting functions, enabling deployment in previously unseen scenarios. We evaluate the resulting blended model on three representative test cases: a turbulent zero-pressure-gradient flat plate, a wall-mounted hump, and a NACA0012 airfoil at various angles of attack, ranging from fully attached to near-stall conditions. Results for these 2D flows show that the proposed strategy adapts to local flow characteristics, effectively leveraging the strengths of individual models and consistently selecting the most suitable expert in each region. Notably, the blended model also demonstrates robustness for flow configurations not included in the training set, underscoring its potential as a practical and generalizable framework for RANS turbulence modeling.

physics.flu-dyn↗

arXiv2024

Space-dependent Aggregation of Stochastic Data-driven Turbulence Models

A stochastic Machine-Learning approach is developed for data-driven Reynolds-Averaged Navier-Stokes (RANS) predictions of turbulent flows, with quantified model uncertainty. This is done by combining a Bayesian symbolic identification methodology for learning stochastic RANS model corrections for selected classes of flows (expert models), and a Mixture-of-Experts methodology that aggregates their predictions. The expert models are learned using the recently proposed SBL-SpaRTA algorithm, which generates sparse analytical expressions of the corrective terms with model parameters described by probability distributions. They outperform the baseline RANS model for flows similar to those used for training, but their generalization to different flows is not warranted. With the aim of quantifying the predictive uncertainty associated with the data-driven models while improving predictive accuracy and generalization capabilities, a space-dependent model aggregation technique (XMA) is then adopted. A gating function, which assigns each model a performance score (weight) based on a vector of local flow features, is trained alongside the expert models. The weights can be interpreted as the probability that a candidate model will outperform its competitors given the flow behavior at a given location. Predictions of unseen flows are formulated as a locally weighted average of the stochastic solutions of the expert models. A prediction uncertainty estimate is obtained by propagating the models' posterior parameter distributions and by evaluating the inter-model prediction variance. The expectancy of the XMA prediction is significantly more accurate than the baseline deterministic solution and the individual solutions of the experts for well-documented benchmark flows not included in the training set, while providing consistent estimates of the predictive variance.

physics.flu-dyn↗