Overview
This tutorial elaborates on our latest field inversion machine learning (FIML) capability for steady-state and time-resolved unsteady flow problems. For more details, please refer to our POF paper.
Fig. 1 Mesh and the vertical probe profile for a 45-degree ramp.
Field inversion machine learning for steady-state flow over the ramp
To run this case, first download tutorials and untar it. Then go to tutorials-master/Ramp/steady/train and run the “preProcessing.sh” script.
./preProcessing.sh
Then, use the following command to run the case:
mpirun -np 4 python runScript_FIML.py 2>&1 | tee logOpt.txt
This case uses our latest FIML interface, which incorporates a neural network model into the CFD solver to compute the augmented field variables (refer to the POF paper for details). We augment the k-omega model and make it match the k-omega SST model. The FIML optimization is formulated as:
Objective function: Regulated prediction error for the bottom wall pressure and the CD values Design variables: Weights and biases for the built-in neural network Augmented variables: betaFIK and betaFIOmega for the k and omega equations, respectively Training configurations: c1: U0 = 10 m/s. c2: U0 = 20 m/s Prediction configuration: U0 = 15 m/s
The optimization converged in 14 iterations, and the objective function reduced from 3.957E+01 to 3.542E+00.
To test the trained model’s accuracy for an unseen flow condition (i.e., U0 = 15 m/s), we can copy the designVariable.json (this file will be generated after the FIML optimization is done.) to tutorials-master/Ramp/steady/predict/trained. Then, go to tutorials-master/Ramp/steady/predict and run Allrun.sh. This command will run the primal for the baseline (k-omega), reference (k-omega SST), and the trained (FIML k-omega) models. The trained will read the optimized neural network weights and biases from designVariable.json, assign them to the built-in neural network model (defined in the regressionModel key in daOption) and run the primal solver.
For the U0 = 15 m/s case, the drag from the reference, baseline, and trained models are: 0.3881, 0.4458, 0.3829, respectively. The trained model significantly improve the drag prediction accuracy for this case.
Field inversion machine learning for time-accurate unsteady flow over the ramp
To run this case, first download tutorials and untar it. Then go to tutorials-master/Ramp/unsteady/train and run the “preProcessing.sh” script.
./preProcessing.sh
Then, use the following command to run the case:
mpirun -np 4 python runScript.py 2>&1 | tee logOpt.txt
The setup is similar to the steady state FIML except that we consider both spatial and temporal evolutions of the flow. In other words, the trained model will improve both spatial and temporal predictions of the flow. We augment the SA model and make it match the k-omega SST model.
Objective function: Regulated prediction error for the bottom wall pressure at all time steps Design variables: Weights and biases for the built-in neural network Augmented variables: betaFINuTilda for the nuTilda equations Training configuration: U0 = 10 m/s Prediction configuration: U0 = 5 m/s
The optimization exited with 50 iterations. The objective function reduced from 4.756E-01 to 3.274E-02.
Once the unsteady FIML is done. We can copy the last dict from designVariableHist.txt to tutorials-master/Ramp/unsteady/predict/trained. Then, go to tutorials-master/Ramp/unsteady/predict and run Allrun.sh. This command will run the primal for the baseline (SA), reference (k-omega SST), and the trained (FIML SA) models, similar to the steady-state case.
The following animation shows the comparison among these prediction case. The trained SA model significantly improves the spatial temporal evolution of velocity fields.
Fig. 2 Comparison among the reference, baseline, and trained models.