A physics-constrained multi-objective CFD-driven model training framework and its application to SWTBLI flows

With growing interest in data-driven turbulence modeling, field inversion and symbolic regression (FISR) have gained attention for producing interpretable correction terms. However, classical FISR lacks fully model-consistent training, limiting predictive accuracy. This study proposes a physics-constrained, multi-objective computational fluid dynamics (CFD)-driven training framework that integrates a CFD solver into gene expression programming for model-consistent training. Correction domains of symbolic expressions are constrained using inversion fields to improve interpretability. The framework is applied to a supersonic compression corner flow using the shear-stress transport (SST) model, yielding the SST-MO model. After appropriate analysis and modification, SST-MO is evaluated on a range of shock-wave/turbulent boundary-layer interaction flows across various Mach numbers, as well as a flat-plate boundary layer to assess its behavior in zero pressure gradient conditions. Classical FISR and single-objective CFD-driven methods are also tested for comparison. Results show that the proposed framework produces a correction model that balances interpretability and predictive performance. Compared to FISR, SST-MO offers improved accuracy, and it maintains greater interpretability than single-objective approaches. The results highlight the potential of multi-objective, physics-informed training for developing practical turbulence model corrections.