CFD-driven symbolic regression of RANS transition models
Abstract
Laminar-turbulent transition governs skin friction, heat transfer and losses in turbomachinery, yet Reynolds-averaged Navier-Stokes (RANS) transition models rely on empirical correlations and hand-calibrated activation functions whose structural deficiencies cannot be resolved by recalibration. We propose a CFD-driven sparse symbolic regression framework to learn interpretable, closed-form corrections to the production and destruction activation functions in the intermittency equation of the local, Galilean-invariant k-ω-γ model of Ge et al. Each correction combines a polynomial of a local pressure-gradient parameter, controlling amplitude and sign, with a bounded exponential of local flow features, controlling spatial support. This construction bounds the corrections without ad hoc limiters. Coefficients are identified by gradient-free optimization with the RANS solver in the loop, accelerated by POD-Kriging field surrogates, using mean-velocity data from wall-resolved large-eddy simulations (LES) of the ERCOFTAC T3 flat-plate cases. Elastic-net hyperparameters are selected automatically through bi-level optimization with leave-one-case-out cross-validation. The resulting model retains 11 of 21 candidate terms, compared with 20 under conventional grid-search tuning, while achieving comparable or slightly better accuracy on training and unseen cases. Both approaches recover the same leading-order correction. Applied without retraining to the transonic LS89 turbine cascade, far beyond the training envelope, the augmented model remains numerically robust and improves heat-transfer predictions at all four operating points, reducing errors by up to 70% where the baseline predicts premature transition under high freestream turbulence. Residual errors in transition onset and length highlight the limits of training on flat-plate data alone.
Related
- Mechanism-Separated Closed-Form Transition Modeling via Field Inversion and Symbolic Regression
- FluxDisco: Symbolic Regression for Stoichiometric Dynamical Systems via Monte Carlo Graph Search
- Physics-Constrained Symbolic Regression for Mean-Velocity and Mixing-Length Scaling in Zero-Pressure-Gradient Turbulent Boundary Layers
- Quantitative schlieren imaging of a laser-ionized plasma channel in atomic vapor using symbolic regression
- From Single Spins to Ensembles: A Calibrated Symbolic Regression Pipeline for NV Spectroscopy
BibTeX
@misc{zemmour2026cfddriven,
title = {{CFD-driven symbolic regression of RANS transition models}},
author = {Louenas Zemmour and Xavier Gloerfelt and Paola Cinnella},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.03210},
eprint = {2611.03210},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.03210},
}
RIS
TY - UNPB
TI - CFD-driven symbolic regression of RANS transition models
AU - Louenas Zemmour
AU - Xavier Gloerfelt
AU - Paola Cinnella
PY - 2026
DA - 2026/11/02
PB - arXiv
DO - 10.48550/arxiv.2611.03210
UR - https://arxiv.org/abs/2611.03210
AB - Laminar-turbulent transition governs skin friction, heat transfer and losses in turbomachinery, yet Reynolds-averaged Navier-Stokes (RANS) transition models rely on empirical correlations and hand-calibrated activation functions whose structural deficiencies cannot be resolved by recalibration. We propose a CFD-driven sparse symbolic regression framework to learn interpretable, closed-form corrections to the production and destruction activation functions in the intermittency equation of the local, Galilean-invariant k-ω-γ model of Ge et al. Each correction combines a polynomial of a local pressure-gradient parameter, controlling amplitude and sign, with a bounded exponential of local flow features, controlling spatial support. This construction bounds the corrections without ad hoc limiters. Coefficients are identified by gradient-free optimization with the RANS solver in the loop, accelerated by POD-Kriging field surrogates, using mean-velocity data from wall-resolved large-eddy simulations (LES) of the ERCOFTAC T3 flat-plate cases. Elastic-net hyperparameters are selected automatically through bi-level optimization with leave-one-case-out cross-validation. The resulting model retains 11 of 21 candidate terms, compared with 20 under conventional grid-search tuning, while achieving comparable or slightly better accuracy on training and unseen cases. Both approaches recover the same leading-order correction. Applied without retraining to the transonic LS89 turbine cascade, far beyond the training envelope, the augmented model remains numerically robust and improves heat-transfer predictions at all four operating points, reducing errors by up to 70% where the baseline predicts premature transition under high freestream turbulence. Residual errors in transition onset and length highlight the limits of training on flat-plate data alone.
ER -