README.md

Seismic inversion: Neural network regularisation using ExternalOperator

This repository is the official implementation of the seismic inversion example in "Escaping the abstraction: a foreign function interface for the Unified Form Language [UFL]", accepted at NeurIPS 2021 (Differentiable Programming workshop) and received the Best Paper award.

Requirements

In order to run the example, you need to have a working firedrake installation.

1. Instructions to install Firedrake can be found here.

2. To install additional requirements:

pip install -r requirements.txt

Seismic inversion

The seismic inversion can be run via the seismic_inversion.py file. When running the file you can specify:

• regulariser: An integer indicating the type of regularisation to take into account: (0: No regularisation, 1: Tikhonov, 2: Neural network)
• scale_noise: Scale factor applied on the noise to make the observed data from the exact solution.
• alpha: Regularisation factor

Run the command:

python seismic_inversion.py -regulariser {regulariser} -scale_noise {scale factor} -alpha {regularisation factor}

You can reproduce the figures of the article via:

python seismic_inversion.py -regulariser 0 1 2

Here are the corresponding figures:

Velocity obtained with: Exact solution (upper left), neural network regularisation (upper right), Tikhonov regularisation (lower left), no regularisation (lower right)

Citation

If you found this work to be useful, then please cite: (arXiv paper)

@article{bouziani-ham-2021-escaping,
    author={Nacime Bouziani and David A. Ham},
    title={Escaping the abstraction: a foreign function interface for the {Unified} {Form} {Language} [{UFL}]},
    year={2021},
    journal={Differentiable Programming workshop at Neural Information Processing Systems 2021}
}