Code to reproduce results in Ziyi Yin, Rafael Orozco, Mathias Louboutin, Felix J. Herrmann, "Solving multiphysics-based inverse problems with learned surrogates and constraints". Published open-access at Advanced Modeling and Simulation in Engineering Sciences. DOI: 10.1186/s40323-023-00252-0

All of the software packages used in this paper are fully open source, scalable, interoperable, and differentiable. The readers are welcome to learn about our software design principles from this open-access article.

We use JUDI.jl for wave modeling and inversion, which calls the highly optimized propagators of Devito.

We use JutulDarcyRules.jl to solve the multiphase flow equations, which calls the high-performant and auto-differentiable numerical solvers in Jutul.jl and JutulDarcy.jl. JutulDarcyRules.jl is designed to interoperate these two packages with other Julia packages in the Julia AD ecosystem via ChainRules.jl.

We use InvertibleNetworks.jl to train the normalizing flows (NFs). This package implements memory-efficient invertible networks via hand-written derivatives. This ensures that these invertible networks are scalable to realistic 3D problems.

We use FNO4CO2.jl to train the Fourier neural operators (FNOs) as learned surrogates for multiphase flow solvers in JutulDarcyRules.jl. In order for scaling to realistic 4D problems, we suggest the readers also have a look at the dfno package, which implements model-parallel Fourier neural operators that are demonstrated to scale to realistic size 4D problems (input size is over $512\times512\times512\times20$).

First, install Julia and Python. The scripts will contain package installation commands at the beginning so the packages used in the experiments will be automatically installed.

There are 12 scripts for permeability inversion with different setups and different types of measurements, listed below.

Also, the script projection-study.jl demonstrates a case study of the relationship between projection in the latent space (expansion or shrinkage) and the accuracy of pre-trained FNO for both in-distribution and out-of-distribution permeability samples.

The software used in this repository can be modified and redistributed according to MIT license.

If you use our software for your research, we appreciate it if you cite us following the bibtex in CITATION.bib.

This repository is written by Ziyi Yin from the Seismic Laboratory for Imaging and Modeling (SLIM) at the Georgia Institute of Technology.

If you have any question, we welcome your contributions to our software by opening issue or pull request.

SLIM Group @ Georgia Institute of Technology, https://slim.gatech.edu.
SLIM public GitHub account, https://github.com/slimgroup.