Investigating Model-Data Inconsistency in Data-Informed Turbulence Closure Terms

Abstract

In the present work, we investigate the stability of turbulence closure predictions from neural network models and highlight the role of model-data-inconsistency during inference. We quantify this inconsistency by applying the Mahalanobis distance and demonstrate that the instability of the model predictions in practical large eddy simulations (LES) correlates with a deviation of the input data between the training dataset and actual simulation data. Moreover, the method of "stability training" is applied to increase the robustness of recurrent artificial neural networks (ANN) against small perturbations in the input, which are typically unavoidable in any practical scenario. We show that this method can increase the stability of simulations with ANN-based closure term predictions significantly. The models also achieve good accuracy on the blind testing set in comparison to the baseline model trained without stability training. The work presented here can thus be seen as a building block towards long-term stable data-driven models for dynamical systems and highlights methods to detect and counter model-data-inconsistencies.

Relexi — A scalable open source reinforcement learning framework for high-performance computing

“…Here, it could be shown that the RL method could provide models that improve on current stateof-the-art turbulence models in terms of accuracy. Moreover, the RL-based agent provided long-term stable simulations, which many other machine learning approaches oftentimes lack [7,3]. The application of Relexi to turbulence modeling is obviously only a first proof-of-concept and will be extended towards other applications in fluid mechanics including shock-capturing [4] or wall-modeling [2] as well as applications in other fields of research.…”