On the Generalizability of Machine-Learning-Assisted Anisotropy Mappings for Predictive Turbulence Modelling

Abstract

Within the context of machine learning-based closure mappings for RANS turbulence modelling, physical realizability is often enforced using ad-hoc postprocessing of the predicted anisotropy tensor. In this study, we address the realizability issue via a new physics-based loss function that penalizes non-realizable results during training, thereby embedding a preference for realizable predictions into the model. Additionally, we propose a new framework for data-driven turbulence modelling which retains the stability and conditioning of optimal eddy viscosity-based approaches while embedding equivariance. Several modifications to the tensor basis neural network to enhance training and testing stability are proposed. We demonstrate the conditioning, stability, and generalization of the new framework and model architecture on three flows: flow over a flat plate, flow over periodic hills, and flow through a square duct. The realizability-informed loss function is demonstrated to significantly increase the number of realizable predictions made by the model when generalizing to a new flow configuration. Altogether, the proposed framework enables the training of stable and equivariant anisotropy mappings, with more physically realizable predictions on new data. We make our code available for use and modification by others.

A data‐driven turbulence modeling for the Reynolds stress tensor transport equation

“…Convolutional NN were used to predict turbulence anisotropy in one‐dimensional flows by Borde et al, 33 although not propagating predictions to the velocity fields. The generalizability of ML on different flow types than those used in training was assessed by McConkey et al 34 The RST predictions were considerably less accurate when extending the ML to unseen flow configurations, indicating that a desired universality in ML models may not be feasible at this moment, with the techniques and data available. As a consequence McConkey et al 34 highlights that the ML corrections should remain limited to similar flows with minor differences, this was also observed by Wang et al 30 The RST was also the target of the NN trained by Zhang et al 35 using the ensemble Kalman method with sparse data.…”

“…The generalizability of ML on different flow types than those used in training was assessed by McConkey et al 34 The RST predictions were considerably less accurate when extending the ML to unseen flow configurations, indicating that a desired universality in ML models may not be feasible at this moment, with the techniques and data available. As a consequence McConkey et al 34 highlights that the ML corrections should remain limited to similar flows with minor differences, this was also observed by Wang et al 30 The RST was also the target of the NN trained by Zhang et al 35 using the ensemble Kalman method with sparse data. The network parameters were updated based on a cost function computed on the discrepancy of the corrected velocity field, rather than on the RST itself.…”

A divide-and-conquer machine learning approach for modeling turbulent flows

“…To progress in this direction of improving generalizability in one brute-force model, the following bottlenecks must be addressed: (i) increasing the amount of training data to encompass different turbulent regimes and flow behaviours for (ii) training a ML model with complex architecture that may accurately account for many degrees of freedom in these various flows [29,30]. Given current computational capabilities, addressing both will be challenging to achieve in the near future.…”