A priori screening of machine-learning turbulence models

Assessing the compliance of a white-box turbulence model with known turbulent knowledge is a straightforward process. It enables users to quickly screen conventional turbulence models and identify any apparent inadequacies, thereby allowing for a more focused and fruitful validation and verification. On the other hand, comparing a black-box machine-learning(ML) model to known empricisms is not straightforward. Unless one implements and tests, it would not be clear if a ML model, trained at finite Reynolds numbers preserves the known high Reynolds number limit. Having to implement a model is inconvenient, particularly when model implementation involves retraining and reinterfacing. This work attempts to address this issue, allowing fast a priori screening of ML models that are based on feed-forward neural networks. The method leverages the mathematical theorems we present in this work. These theorems offer estimates of a network's limits even when the exact weights and biases are unknown. In this work, we screen existing ML wall models and RANS models for their compliance with the logarithmic law in an a priori manner. In addition to enabling fast screening of existing models, the theorems also provide guidelines for future ML models.