Gappy AE

This repository contains Jupyter notebooks for numerical examples of the paper titled "Gappy Data Reconstruction using Unsupervised Learning for Digital Twin". Note that an open-source FEM solver, MFEM was used to generate training data. Please refer to the paper for more details. Since the size of the training data is large, we do not upload it here. The training data will be provided upon request via email at youngkyu_kim@berkeley.edu.

Requirements

This repository has been tested with Ubuntu Server 22.04, CUDA 12.1, pytorch 2.2.1 environment.

Installing PyTorch
PyTorch must be installed by following the installation guide on the PyTorch Official Website.

Installing Sparse Linear
Sparse Linear modules are designed to efficiently handle operations on sparse matrices.

Packages required by the project can be installed using the following command:

  pip3 install sparselinear torch-scatter torch-sparse

Data Generation

GappyAE
To clone this repository, open your terminal and run the following command:

git clone https://github.com/youngkyu-kim/GappyAE.git

LaSDI
Clone the LaSDI repository and build it with the source codes and makefiles provided. Place the cloned repository into your preferred directory :

1. Navigate to the directory where you want to place the LaSDI project.

2. Run the following command to clone the repository or Download:

   git clone https://github.com/LLNL/LaSDI.git

Once cloned, navigate into the LaSDI directory and build : ./setup.sh

1. Move to your installed directory:

cd path/to/your/LaSDI

2. Remove the existing directories:

rm -r Radial\ Advection Diffusion

3. Copy ex16_diffusion, ex23_wave, and ex9_advection directories in 1_Data_Generation to your LaSDI:

cp -r path/to/your/GappyAE/1_Data_Generation/*  path/to/your/LaSDI

4. Navigate into the ex16_diffusion, ex23_wave, and ex9_advection directory and change mode of bash_ex16.sh, bash_ex23.sh, bash_ex9.sh, respectively:

chmod +x bash_exXX.sh

./bash_exXX.sh

5. Move the data directory to the GappyAE/__data directory as separate directories once the build is complete:

cp -r ex9_advection/data/* GappyAE-main/__data/ex9_advection/
cp -r ex16_diffusion/data/* GappyAE-main/__data/ex16_diffusion
cp -r ex23_wave/data/* GappyAE-main/__data/ex23_wave

Below figures show five snapshots for two extreme parameter values.

Diffusion simulation solutions from the initial to the final time for param=0.75

Diffusion simulation solutions from the initial to the final time for param=1.25

Advection simulation solutions from the initial to the final time for param=0.75

Advection simulation solutions from the initial to the final time for param=1.25

Wave simulation solutions from the initial to the final time for param=0.75

Wave simulation solutions from the initial to the final time for param=1.25

Model Training

AE
To find nonlinear manifold denoted as function $g(\hat{x})$, you need to train auto-encoders.

1. Move to 2_Model_Training folder and run train_NM_XXX.ipynb
2. Trained models are saved in __model

POD
To find POD basis denoted as function $\Phi$, you need to do SVD.

1. Move to 2_Model_Training folder and run train_LS_XXX.ipynb
2. Trained models are saved in __model

Data Reconstruction

Gappy AE

1. Move to 3_Data_Reconstruction folder and run gappyAE_[PROBLEM_TYPE]_[MEASUREMENT_REGION]_[SAMPLING_ALGORITHM].ipynb

• [PROBLEM_TYPE]: diffusion/advection/wave
• [MEASUREMENT_REGION]: inner/bndry
• [SAMPLING_ALGORITHM]: uniform/LHS/DEIM/*SOPT

Gappy POD

1. Move to 3_Data_Reconstruction folder and run gappyPOD_[PROBLEM_TYPE]_[MEASUREMENT_REGION]_[SAMPLING_ALGORITHM].ipynb

• [PROBLEM_TYPE]: diffusion/advection/wave
• [MEASUREMENT_REGION]: inner/bndry
• [SAMPLING_ALGORITHM]: uniform/LHS/DEIM/*SOPT

*Note: You need to build pylibROM and run python scripts in SOPT_scripts folder to get SOPT sample points. If you want to skip this step, you can use the SOPT sample points that are provided in 2.5_SOPT/SOPT_sample_points folder.

SOPT(optional)

build pylibROM in docker container

sudo docker pull ghcr.io/llnl/librom/librom_env:latest

mkdir pylibROM_docker && cd pylibROM_docker

git clone https://github.com/LLNL/libROM.git && git clone --recurse-submodules https://github.com/llnl/pylibROM.git

cp -r path/to/your/GappyAE-main/2.5_SOPT/* pylibROM_docker/pylibROM/tests

sudo docker run -it -v $HOME/pylibROM_docker:/home/test/ ghcr.io/llnl/librom/librom_env:latest

cd pylibROM

sudo apt install python-is-python3

sudo pip install --upgrade pip==23.2.1

sudo pip install ./

cd tests

sudo ./run_SOPT.sh

exit

cd path/to/your/pylibROM_docker

cp -r tests/SOPT_scripts/SOPT_sample_points path/to/your/GappyAE/__model

Paper

Kim, Y., Choi, Y., & Yoo, B. (2023). Gappy Data Reconstruction using Unsupervised Learning for Digital Twin. arXiv preprint arXiv:2312.07902.

Citation

@article{kim2023gappy,
  title={Gappy Data Reconstruction using Unsupervised Learning for Digital Twin},
  author={Kim, Youngkyu and Choi, Youngsoo and Yoo, Byounghyun},
  journal={arXiv preprint arXiv:2312.07902},
  year={2023}
}

Authors

• Youngkyu Kim (KIST)
• Hyeokmin Lee (KIST)