@Article{CiCP-30-5,
author = {Ströfer, Michelén, Carlos, A. and Zhang, Xin-Lei and Xiao, Heng},
title = {Ensemble Gradient for Learning Turbulence Models from Indirect Observations},
journal = {Communications in Computational Physics},
year = {2021},
volume = {30},
number = {5},
pages = {1269--1289},
abstract = {<p style="text-align: justify;">Training data-driven turbulence models with high fidelity Reynolds stress
can be impractical and recently such models have been trained with velocity and pressure measurements. For gradient-based optimization, such as training deep learning
models, this requires evaluating the sensitivities of the RANS equations. This paper
explores the use of an ensemble approximation of the sensitivities of the RANS equations in training data-driven turbulence models with indirect observations. A deep
neural network representing the turbulence model is trained using the network’s gradients obtained by backpropagation and the ensemble approximation of the RANS
sensitivities. Different ensemble approximations are explored and a method based on
explicit projection onto the sample space is presented. As validation, the gradient approximations from the different methods are compared to that from the continuous adjoint equations. The ensemble approximation is then used to learn different turbulence
models from velocity observations. In all cases, the learned model predicts improved
velocities. However, it was observed that once the sensitivity of the velocity to the
underlying model becomes small, the approximate nature of the ensemble gradient
hinders further optimization of the underlying model. The benefits and limitations of
the ensemble gradient approximation are discussed, in particular as compared to the
adjoint equations.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2021-0082},
url = {https://global-sci.com/article/79602/ensemble-gradient-for-learning-turbulence-models-from-indirect-observations}
}