Explainable Data-Driven RANS Closures for Turbulence Modeling

Scientific Machine Learning is transforming turbulence modeling, particularly for Reynolds-

averaged Navier–Stokes (RANS) closures, which are crucial for simulating compressible fluid

flows. Despite their widespread use, RANS models often suffer from model-form errors that lead

to significant inaccuracies. Building on the foundational work of Parish et al. [AIAA 2023-2126;

https://doi.org/10.2514/6.2023-2126], this study integrates explainable machine learning

techniques with rigorous sensitivity analysis to improve the reliability of RANS turbulence

closures.

Utilizing multi-step training across eight diverse datasets—including channel flows at various

Reynolds numbers, duct flow, and hypersonic boundary layers—this research investigates

discrepancies in Reynolds stress predictions. We emphasize hyperparameter sensitivity and

evaluate model performance on out-of-distribution datasets, ensuring robust findings. Our analysis

reveals that shear components of the anisotropy tensor are critical for enhancing prediction

accuracy, particularly in wall-bounded and hypersonic flows. To elucidate model behavior, we

employ SHAP (SHapley Additive exPlanations) analysis, providing insights into the influence of

input features on predictions. This transparency fosters confidence in deploying machine learning

techniques in critical applications. We also explore LIME (Local Interpretable Model-Agnostic

Explanations) for local sensitivity assessments, complementing our SHAP findings.

This study advances turbulence modeling through data-driven approaches and contributes to fluid

dynamics and machine learning by ensuring models are interpretable, reliable, and grounded in

established physical principles. The implications extend beyond specific applications, enhancing

the credibility and applicability of RANS simulations in mission-critical contexts, such as

aerospace and energy systems. This work is supported by the DOE-NNSA ASC program.