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OpenFOAM MachineLearning Hackathon- Team 3 & 4

The objective was to implement a data driven and physics driven neural network for inferring potential flow given sparse data points from the bulk. This was achieved by integrating inbuilt functions of the PyTorch C++ API with OpenFOAM.

Team 3 Members

Team 4 Members

Supervisors

  • Tomislav Maric
  • Andre Weiner

Dependencies

For the OpenFOAM and libtorch installation check README.md

For the other python scripts used here in the repository: python >= 3.7 requirements.txt - for Bayesian Optimisation

Procedure

  1. Copy the pinnFoam application into the pinnPotentialFoam application, rename it + compile it.

    • Rename the pinnFoam to pinnPotentialFoam.
    • Rename all pinnFoams in the code to pinnPotentialFoam. grep -r pinnFoam

  2. Edit createFields.H and read the potientialFoam fields Phi and U.

  3. Adapt the Neural Network (NN) $\Psi(x,y,z,\theta)$ to map a point in space $\boldsymbol{x} =(x,y,z)$ to the output vector $O=(\Phi,U_x, U_y, U_z)$, with $\boldsymbol{U}=(U_x, U_y, U_z)$ being the potential-flow velocity, and $\Phi$ the velocity-potential.

  4. Remove the existing PiNN residual MSE and train the NN as a Multilayer Perceptron on the Phi and U fields computed by OpenFOAM’s potentialFoam solver.

  5. Extend the NN into a PiNN for potential flow, by programming the potential-flow PDE residual

    This means:

    • Implementing the Laplace operator for $\Phi$.
    • Implementing the divergence operator for $\boldsymbol{U}$.
    • Combining both into the residual MSE, and summing the residual MSE with the data MSE.

File structure

physics-based-dl-solution-03-4/
---applications/
   ---pinnFoam
   ---pinnFoamSetSphere
   ---dnnPotentialFoam
   ---pinnPotentialFoam
---run/
   ---Cylinder
   ---dnnCylinder
   ---pinnCylinder
   ---dnnCylinderHOPT_grid
   ---dnnCylinderHOPT_bayes
   ---pinnCylinderHOPT_grid
   ---pinnCylinderHOPT_bayes
---README.md
---Allrun
---Allmake
---Allclean
---Presentation.pdf
---ProjectReport.pdf

Code Changes in OpenFOAM

According to the physics of the problem and solver, there has been changes made in different dictionaries.

Optimization

Bayesian Optimization has been implemented to the solver.

How to use

Follow this procedure to run the code and see the results.

open the terminal and navigate Cylinder testcase and execute the command below:

cd run/unit_box_domain/cylinder

./Allclean

./Allrun

pinnPotentialFoam

paraFoam

Results

CPU time and accuracy of using the NN as the MLP without the PiNN residual and the PiNN approach for approximating Psi ,u is being compared.