A priori screening of data-enabled turbulence models

TL;DR

This paper introduces a mathematical framework for rapidly screening machine-learning turbulence models against known physical laws, facilitating validation without full model implementation.

Contribution

It presents theorems that estimate neural network limits, enabling a priori screening of ML turbulence models for physical compliance.

Findings

Screened existing ML wall models for physics compliance

Provided guidelines for future ML turbulence model development

Demonstrated the effectiveness of the theorems in model validation

Abstract

Assessing the compliance of a white-box turbulence model with known turbulent knowledge is straightforward. It enables users to screen conventional turbulence models and identify apparent inadequacies, thereby allowing for a more focused and fruitful validation and verification. However, comparing a black-box machine-learning model to known empirical scalings is not straightforward. Unless one implements and tests the model, it would not be clear if a machine-learning model, trained at finite Reynolds numbers preserves the known high Reynolds number limit. This is inconvenient, particularly because model implementation involves retraining and re-interfacing. This work attempts to address this issue, allowing fast a priori screening of machine-learning models that are based on feed-forward neural networks (FNN). The method leverages the mathematical theorems we present in the paper. These theorems offer estimates of a network's limits even when the exact weights and biases are unknown. For demonstration purposes, we screen existing machine-learning wall models and RANS models for their compliance with the log layer physics and the viscous layer physics in a priori manner. In addition, the theorems serve as essential guidelines for future machine-learning models.