[Paper Review] An Old-Fashioned Framework for Machine Learning in Turbulence Modeling

Philippe R. Spalart|arXiv (Cornell University)|Aug 1, 2023

Meteorological Phenomena and Simulations12 citations

TL;DR

The paper offers a practical framework and guidance for ML in turbulence modeling, emphasizing physics-based constraints, turbulence culture, and product-focused CFD over purely publishable results, with a concrete DNS-data example.

ABSTRACT

The objective is to provide clear and well-motivated guidance to Machine Learning (ML) teams, founded on our experience in empirical turbulence modeling. Guidance is also needed for modeling outside ML. ML is not yet successful in turbulence modeling, and many papers have produced unusable proposals either due to errors in math or physics, or to severe overfitting. We believe that "Turbulence Culture" (TC) takes years to learn and is difficult to convey especially considering the modern lack of time for careful study; important facts which are self-evident after a career in turbulence research and modeling and extensive reading are easy to miss. In addition, many of them are not absolute facts, a consequence of the gaps in our understanding of turbulence and the weak connection of models to first principles. Some of the mathematical facts are rigorous, but the physical aspects often are not. Turbulence models are surprisingly arbitrary. Disagreement between experts confuses the new entrants. In addition, several key properties of the models are ascertained through non-trivial analytical properties of the differential equations, which puts them out of reach of purely data-driven ML-type approaches. The best example is the crucial behavior of the model at the edge of the turbulent region (ETR). The knowledge we wish to put out here may be divided into "Mission" and "Requirements," each combining physics and mathematics. Clear lists of "Hard" and "Soft" constraints are presented. A concrete example of how DNS data could be used, possibly allied with ML, is first carried through and illustrates the large number of decisions needed. Our focus is on creating effective products which will empower CFD, rather than on publications.

Motivation & Objective

• Provide clear, well-motivated guidance for ML teams in turbulence modeling.
• Highlight the limitations of ML in turbulence and the value of physics-informed constraints.
• Introduce a framework combining physics and mathematics to guide model development.
• Illustrate how DNS data can be used within this framework to inform decisions.
• Focus on producing usable CFD products rather than purely academic publications.

Proposed method

• Split the guidance into Mission and Requirements, combining physics and mathematics.
• Present clear lists of hard and soft constraints for models.
• Provide a concrete DNS-data example to illustrate data-use decisions and workflow.
• Discuss the edge behavior of turbulence models, such as at the edge of the turbulent region (ETR).
• Argue for integrating traditional modeling thinking with ML rather than relying solely on data-driven approaches.

Experimental results

Research questions

• RQ1 What constitutes a usable and principled framework for ML in turbulence modeling?
• RQ2 How should hard and soft constraints be defined and enforced in turbulence models?
• RQ3 How can DNS data be effectively integrated into an ML-based turbulence modeling workflow?
• RQ4 What are the practical challenges and decisions that determine whether an ML approach is publishable versus product-ready in CFD?

Key findings

• The paper provides explicit lists of hard and soft constraints for turbulence modeling.
• It argues that turbulence culture (TC) requires years to learn and cannot be easily conveyed, impacting ML adoption.
• A concrete DNS-data example is used to show the many decisions required when combining ML with traditional modeling.
• The focus is on creating effective CFD products rather than pursuing publications.
• It highlights that some mathematical facts are rigorous but physical aspects are not, and that model behavior at critical regions (ETR) is non-trivial.