README.md

SIAM MPI23 Project "Model inversion for complex physical systems using low-dimensional surrogates"

Instructions

1. Clone this repository and navigate to your local copy

2. Install Miniforge and choose to not initialize Miniforge by running conda init. No need to polute your runcom files. For macOS and bash this looks like:

   a. Download the installation script and run it:

   bash Miniforge3-MacOSX-arm64.sh
   

   b. Accept the license

   c. Specify an installation location

   d. Say no to Do you wish the installer to initialize Miniforge3 by running conda init?

3. Initialize conda. For the previous example, this looks like

   eval "$(MINIFORGE3_INSTALL_DIR/bin/conda shell.bash hook)"
   

4. Create the conda-forge environment pnnl_mpi23:

   conda env create -f environment.yml
   

5. Activate the pnnl_mpi23 environment

   conda activate pnnl_mpi23
   

6. Download the data file mpi23_ens_data.h5 from the Zenodo repository and place it on the data folder

7. Verify the checksums

   cd data; sha256sum -c SHA256SUMS; cd ..
   

8. Launch JupyterLab and start!

   jupyter lab
   

Checkout the notebook file notebooks/data_read_example.ipynb to see how to read the data and start working with it.

HDF5 data file

This file contains the following datasets:

• Nens: Number of data pairs
• Nxi: Number of terms of the Kosambi-Karhunen-Loève (KKL) expansion of the log-transmissivity field
• xi_ens: Nens vectors of KKL coefficients
• u_ens: Nens vectors of discretized pressure fields
• ytms_ens: Nens vectors of discretized log-transmissivity fields, corresponding to the entries of xi_ens, minus the true field's mean
• ytm: The true log-transmissivity field's mean
• yref: The true log-transmissivity field minus its mean
• ypred, Psi_y: The KKL mean and matrix of coefficients

The entries of xi_ens and ytms_ens are related by the KKL:

ytms_ens[i] = ypred + Psi_y @ xi_ens[i]

Any of the log-transmissivity fields can be recovered by adding the true field's mean:

ytm + yref        # The true log-transmissivity field
ytm + ytms_ens[i] # The ith log-transmissivity field in the dataset