FNO4CO2

This repository contains the implementation of learned coupled inversion framework and the numerical experiments in Learned coupled inversion for carbon sequestration monitoring and forecasting with Fourier neural operators, accepted by the International Meeting for Applied Geoscience & Energy 2022.

The aforementioned framework entails a re-implementation of Fourier neural operators from Fourier Neural Operator for Parameter Partial Differential Equations authored by Zongyi Li et al. The original repository is in python.

This code is based on the Julia Language and the package DrWatson to make a reproducible scientific project named

FNO4CO2

To (locally) reproduce this project, do the following:

1. Download this code base. Notice that raw data are typically not included in the git-history and may need to be downloaded independently.
2. Download python and Julia. The numerical experiments are reproducible by python 3.7 and Julia 1.7.
3. Install Devito, a python package used for wave simulation.
4. Open a Julia console and do:

   julia> using Pkg
   julia> Pkg.activate("path/to/this/project")
   julia> Pkg.instantiate()
   

This will install all necessary Julia packages for you to be able to run the scripts and everything should work out of the box.

Examples

The repository currently includes several scripts.

gen_perm.jl generates random permeability samples and gen_conc.jl generates time-varying CO2 concentration for each of them using the numerical simulator from FwiFlow.jl. To save you some time to reproduce our examples, we've also provided the dataset through a dropbox link -- when you run the network training script, the dataset will be downloaded automatically.

fourier_3d.jl trains a 3D FNO which maps the permeability to time-varying CO2 concentration governed by two-phase flow equations, with the dataset generated by gen_perm.jl and gen_conc.jl. You can train the FNO on GPU if available by setting the env variable export FNO4CO2GPU=1 in your environment (e.g. in ~/.zshrc on my mac, or just do FNO4CO2GPU=1 julia). The trained 3D network for the two-phase flow example is provided in the repository under data/3D-FNO.

fourier_3d_grad.jl script shows how to conduct a learned inversion to estimate the permeability (input of FNO) from the CO2 concentration snapshots. It uses gradient descent with back-tracking line search to iteratively invert the FNO.

learned_coupled_inversion.jl script shows how to conduct a learned coupled inversion, i.e. we invert for the permeability from time-lapse seismic datasets. The process involves inverting multiple physics as shown in Coupled Time-Lapse Full-Waveform Inversion for Subsurface Flow Problems Using Intrusive Automatic Differentiation, while it uses a pre-trained FNO as a surrogate for the fluid-flow solver.

Citation

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

Acknowledgements

We thank the developers from several software packages in the open-source software community, which we based our implementation on. The FNO is re-implemented following Zongyi Li et al's work in https://github.com/zongyi-li/fourier_neural_operator. The two-phase flow dataset is generated by FwiFlow.jl. We use Devito and JUDI.jl for wave simulations. We use SetIntersectionProjection for constrained optimization.

This research was carried out with the support of Georgia Research Alliance and partners of the ML4Seismic Center.

Author

Ziyi (Francis) Yin, [email protected]