This repo contains the code and data used to generate the results in the report:
J. Warner, J. Cuevas, G. Bomarito, P. Leser, and W. Leser. Inverse Estimation of Elastic Modulus
Using Physics-Informed Generative Adversarial Networks. NASA/TM-2020-5001300. May 2020.
- Python 3
- Tensorflow 2
All additional modules required that can be found in requirements.txt
pip install -r requirements.txtThe training/testing data used for the report can be found in the data/ directory,
so this step is optional. If you would like to create your own data (change the
number of sensors, collocation points, etc. used), see the generate_pigan.py script.
Use the train_pigan.py file to train the PIGAN using the generated training data. To visualize realtime metrics, use Tensorboard. Use the command:
tensorboard --logdir "data/tensorboard/"
and then follow the link provided in Chrome to see the graphs.
To generate samples with the trained PIGAN and assess accuracy versus the testing data,
use the evaluate_pigan.py script. Be sure to specify the location of your trained models,
or use the models in the paper, which reside in the data/paper_models/ folder.
This python script will generate data using the model and recreate many of the
report. After the script runs, the plots will be saved as pdfs in data/plots/.
The Generator is composed of two feed forward deep neural networks (DNNs) that generate values for u and E, respectively.
It learns to estimate the probability distribution through 3 seperate loss terms:
WGAN Loss is the loss associated with the Discriminator:
PDE Loss is found by evaluating the generated samples at collocation points and computing the PDE's residual:
The residual is then averaged over all samples and collocation points:
The implementation of PDE loss can be found in pde.py.
Boundary Condition Loss is calculated similarly. First generated samples are evaulated at collocation points on the boundary:
The residual is then averaged over all samples and boundary collocation points:
The implementation of Boundary Condition loss can be found boundary_conditions.py.
These losses are combined to find the Total Loss: (Note: Our results equally weighted all three loss types)
The Discriminator looks at the samples of u being generated and scores them on how close they are to the real expected values of u.
It also enforces the gradient penalty, which encourages the discriminator gradients towards unity:
See the report for more details on the PIGAN formulation.
- The authors thank Theodore Lewitt (USC) for his help in preparing the code in this repo.