[论文解读] An Old-Fashioned Framework for Machine Learning in Turbulence Modeling

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

Meteorological Phenomena and Simulations被引用 12

一句话总结

本文提供了一个实用框架和指南，用于在湍流建模中的机器学习，强调基于物理的约束、湍流文化，以及面向产出的CFD，而不仅仅是可发表的结果，并附有一个具体的DNS数据示例。

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.

研究动机与目标

• 为湍流建模中的 ML 团队提供清晰且有充分动机的指导。
• 强调 ML 在湍流中的局限性以及物理信息约束的价值。
• 引入一个结合物理学与数学以指导模型开发的框架。
• 说明在该框架内如何使用 DNS 数据来为决策提供信息。
• 着重于产生可用的 CFD 产品，而不仅仅是学术论文。

提出的方法

• 将指导分为 Mission 与 Requirements，将物理学与数学相结合。
• 给出模型的硬约束和软约束的清晰列表。
• 提供一个具体的 DNS 数据示例，以说明数据使用决策与工作流程。
• 讨论湍流模型在边缘行为，如在湍流区域边缘（ETR）处的边缘行为。
• 主张将传统建模思维与 ML 相结合，而不是单纯依赖数据驱动的方法。

实验结果

研究问题

• RQ1 什么样的框架才是可用且有原则性的湍流建模中 ML 的框架？
• RQ2 应如何定义并执行湍流模型中的硬约束和软约束？
• RQ3 如何在基于 ML 的湍流建模工作流中有效整合 DNS 数据？
• RQ4 在 CFD 中，决定一个 ML 方法是可发表还是可用于产品的实际挑战与决策有哪些？

主要发现

• 本文提供了湍流建模的硬约束和软约束的明确列表。
• 它认为湍流文化（TC）需要多年学习且难以传授，这影响了 ML 的应用。
• 使用一个具体的 DNS 数据示例来展示将 ML 与传统建模结合时所需的众多决策。
• 重点在于创建有效的 CFD 产品，而不是追求发表论文。
• 它强调一些数学事实是严格的，但物理方面并非如此，且模型在关键区域（ETR）的行为并非简单。