Parameter Identification of RANS Turbulence Model Using Physics-Embedded Neural Network

Shirui Luo, Madhu Vellakal, Seid Koric, Volodymyr Kindratenko, Jiahuan Cui

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Identifying the appropriate parameters of a turbulence model for a class of flow usually requires extensive experimentation and numerical simulations. Therefore even a modest improvement of the turbulence model can significantly reduce the overall cost of a three-dimensional, time-dependent simulation. In this paper we demonstrate a novel method to find the optimal parameters in the Reynolds-averaged Navier–Stokes (RANS) turbulence model using high-fidelity direct numerical simulation (DNS) data. A physics informed neural network (PINN) that is embedded with the turbulent transport equations is studied, physical loss functions are proposed to explicitly impose information of the transport equations to neural networks. This approach solves an inverse problem by treating the five parameters in turbulence model as random variables, with the turbulent kinetic energy and dissipation rate as known quantities from DNS simulation. The objective is to optimize the five parameters in turbulence closures using the PINN leveraging limited data available from costly high-fidelity DNS data. We validated this method on two test cases of flow over bump. The recommended values were found to be Cϵ1 = 1.302, Cϵ2 = 1.862, Cμ = 0.09, σK = 0.75, σϵ = 0.273; the mean absolute error of the velocity profile between RANS and DNS decreased by 22% when using these neural network inferred parameters.
Original languageEnglish (US)
Title of host publicationHigh Performance Computing - ISC High Performance 2020 International Workshops, Revised Selected Papers
Subtitle of host publicationISC High Performance 2020 International Workshops, Frankfurt, Germany, June 21–25, 2020, Revised Selected Papers
EditorsHeike Jagode, Hartwig Anzt, Guido Juckeland, Hatem Ltaief
Number of pages13
ISBN (Electronic)978-3-030-59851-8
ISBN (Print)978-3-030-59850-1
StatePublished - Oct 20 2020

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume12321 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


  • Neural network
  • Physics embedded machine learning
  • Turbulence modeling

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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