On the Generalizability of Machine-Learning-Assisted Anisotropy Mappings for Predictive Turbulence Modelling

Abstract

Several machine learning frameworks for augmenting turbulence closure models have been recently proposed. However, the generalizability of an augmented turbulence model remains an open question. We investigate this question by systematically varying the training and test sets of several models. An optimal three-term tensor basis expansion is used to develop a model-agnostic data-driven turbulence closure approximation. Then, hyperparameter optimization is performed for a random forest, a neural network, and an eXtreme Gradient Boosting (XGBoost) model. We recommend XGBoost for data-driven turbulence closure modelling owing to its low-tuning cost and good performance. We also find that machine learning models generalize well to new parametric variations of flows seen in the training dataset, but lack generalizability to new flow types. This generalizability gap suggests that machine learning methods are most suited for developing specialized models for a given flow type, a problem often encountered in industrial applications.

Keywords:

• Computational fluid dynamics
• data-driven turbulence closure
• deep-learning neural networks
• gradient boosting
• hyperparameter optimization
• machine learning generalizability
• random forest

Acknowledgements

The authors wish to thank the anonymous reviewers for their careful review of our manuscript and helpful suggestions.

Data Availability

All data used in this study are from an open-source turbulence modelling dataset on Kaggle: https://doi.org/10.34740/kaggle/dsv/2637500. All code used in this investigation is available on github: https://github.com/rmcconke/optimal_tensor_basis.

Disclosure statement

The authors report there are no competing interests to declare.

Additional information

Funding

R.M. was supported by the Ontario Graduate Scholarship (OGS) program and the Natural Sciences and Engineering Research Council of Canada (NSERC). The computational resources for this work were supported by the Tyler Lewis Clean Energy Research Foundation (TLCERF) and the Shared Hierarchical Academic Research Computing Network (SHARCNET).