Our solution for the physics-based-dl part of OpenFOAM Machine Learning Hackathon. We adapted the Neural Network (NN) $\Psi(x,\ y,\ z,\ \theta)$ to map the cell center field $\mathbf{x}= (x,\ y,\ z)$ to the output vector field $\mathbf{o}= (\phi,\ u_x,\ u_y,\ u_z)$, where $\phi$ is the velocity potential and $\mathbf{u}=(\ u_x,\ u_y,\ u_z)$ is the velocity. Different losses are tested:
To invesgite the impact of $LOSS$ on the results, three combinations are implemented: $LOSS = LOSS_{data}$, $LOSS = LOSS_{data} + LOSS_{residual1}$, $LOSS = LOSS_{data} + LOSS_{residual1} + LOSS_{residual2}$.
The training data are from the cylinder case of potentialFoam.