Bayesian optimization based on Gaussian processes (BO-GP) for CFD simulations.

The BO-GP codes are developed using GPy and GPyOpt. The optimizer is non-intrusive and can be linked to any CFD solver.


Y. Morita, S. Rezaeiravesh, N. Tabatabaeia, R. Vinuesaa, K. Fukagata, P. Schlatter, Applying Bayesian Optimization with Gaussian Process Regression to Computational Fluid Dynamics Problems, Journal of Computational Physics, 2021.

Exmaple: Turbulent boundary layer (TBL) with non-zero pressure gradient.

See Section 5 in the above reference. The flow is simulated using OpenFOAM.


Questions can be forwarded to [email protected], [email protected], and [email protected].

List of included files and folders:

  • main driver for running the example, i.e. BO-GP of pessure-gradient TBL simulated by OpenFOAM.

  • gpOptim/: Bayesian optimization codes based on Gaussian processes, using GPy and GPyOpt.

    • workDir/
      • gpList.dat
  • OFcase/: OpenFOAM case folder

    • system/
      • (written in, used by blockMeshDict & controlDict).
      • blockMeshDict
      • controlDict
      • decomposeParDict
      • fvSchemes
      • fvSolution
    • 0/
      • U,p,k,omega,nut
      • *_IC files (use to make these files).
    • constant/
      • polyMesh/ (not included)
      • transportProperties
    • jobscript
  • OFpost/: Post-processing the results of OFcase.

  • OFpre/: Pre-processing the OFcase

    • creating using the latest parameter sample.
    • inflow/ Creating inflow conditions for RANS of TBL with pressure gradient using DNS data for the TBL with zero-pressure gradient.
  • figs/: To save figures produced when running the optimization.

    • make movie in png/ from pdf files.
  • data/: Created when running the BO-GP.

  • storage/: Created when running the BO-GP.

Settings & inputs (to run the example):

  • In U_infty, delta99_in, Nx, Ny, Nz, t, loop params, path, beta_t etc.
  • /gpOptim/ number of parameters, range of parameters, tolerance, GP kernel, xi, etc.


  1. python3.X
  2. numpy
  3. matplotlib
  4. GPy
  5. GpyOpt
  6. OpenFOAM v.7 (or v.6)
  7. bl_data/ in OFpre/inflow/ (DNS data from here)

How to test the example for different settings:

  • To change the structure of the geometry

    • create the new inflow from precursor using OFpre/inflow/ (precursor results required)
    • update the blockMeshDict
    • update the driver accordingly
  • To change the number of prosessors used for the OpenFOAM simulation

    • update nProcessors in the driver
    • update decomposeParDict
    • update jobScript
  • To change the parameterization of the upper wall

    • change qBound in
    • update blockMeshDict
  • To change beta_t (target pressure-gradient parameter beta)

    • change beta_t in the driver
  • When you clone this repository and get errors, please try run:

    • mkdir data
    • mkdir storage
    • mkdir OFcase/constant/polyMesh/


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