TY - JOUR

T1 - Embedded training of neural-network subgrid-scale turbulence models

AU - MacArt, Jonathan F.

AU - Sirignano, Justin A

AU - Freund, Jonathan B.

N1 - Funding Information:
This material is based in part upon work supported by the Department of Energy, National Nuclear Security Administration, under Award No. DE-NA0002374. This research is part of the Blue Waters sustained-petascale computing project, which is supported by the National Science Foundation (Awards No. OCI-0725070 and No. ACI-1238993) and the State of Illinois. Blue Waters is a joint effort of the University of Illinois at Urbana-Champaign and its National Center for Supercomputing Applications.
Publisher Copyright:
© 2021 American Physical Society.

PY - 2021/5

Y1 - 2021/5

N2 - The weights of a deep neural-network model are optimized in conjunction with the governing flow equations to provide a model for subgrid-scale stresses in a temporally developing plane turbulent jet at Reynolds number Re0=6000. The objective function for training is first based on the instantaneous filtered velocity fields from a corresponding direct numerical simulation, and the training is by a stochastic gradient descent method, which uses the adjoint Navier-Stokes equations to provide the end-to-end sensitivities of the model weights to the velocity fields. In-sample and out-of-sample testing on multiple dual-jet configurations show that its required mesh density in each coordinate direction for prediction of mean flow, Reynolds stresses, and spectra is half that needed by the dynamic Smagorinsky model for comparable accuracy. The same neural-network model trained directly to match filtered subgrid-scale stresses, without the constraint of being embedded within the flow equations during the training, fails to provide a qualitatively correct prediction. The coupled formulation is generalized to train based only on mean-flow and Reynolds stresses, which are more readily available in experiments. The mean-flow training provides a robust model, which is important, though a somewhat less accurate prediction for the same coarse meshes, as might be anticipated due to the reduced information available for training in this case. The anticipated advantage of the formulation is that the inclusion of resolved physics in the training increases its capacity to extrapolate. This is assessed for the case of passive scalar transport, for which it outperforms established models due to improved mixing predictions.

AB - The weights of a deep neural-network model are optimized in conjunction with the governing flow equations to provide a model for subgrid-scale stresses in a temporally developing plane turbulent jet at Reynolds number Re0=6000. The objective function for training is first based on the instantaneous filtered velocity fields from a corresponding direct numerical simulation, and the training is by a stochastic gradient descent method, which uses the adjoint Navier-Stokes equations to provide the end-to-end sensitivities of the model weights to the velocity fields. In-sample and out-of-sample testing on multiple dual-jet configurations show that its required mesh density in each coordinate direction for prediction of mean flow, Reynolds stresses, and spectra is half that needed by the dynamic Smagorinsky model for comparable accuracy. The same neural-network model trained directly to match filtered subgrid-scale stresses, without the constraint of being embedded within the flow equations during the training, fails to provide a qualitatively correct prediction. The coupled formulation is generalized to train based only on mean-flow and Reynolds stresses, which are more readily available in experiments. The mean-flow training provides a robust model, which is important, though a somewhat less accurate prediction for the same coarse meshes, as might be anticipated due to the reduced information available for training in this case. The anticipated advantage of the formulation is that the inclusion of resolved physics in the training increases its capacity to extrapolate. This is assessed for the case of passive scalar transport, for which it outperforms established models due to improved mixing predictions.

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U2 - 10.1103/PhysRevFluids.6.050502

DO - 10.1103/PhysRevFluids.6.050502

M3 - Article

AN - SCOPUS:85106350736

VL - 6

JO - Physical Review Fluids

JF - Physical Review Fluids

SN - 2469-990X

IS - 5

M1 - 050502

ER -