learning-eit

learning-eit contains the code used to reproduce the numerical experiments in the paper "Extension and neural operator approximation of the electrical impedance tomography inverse map." It includes:

• Training and evaluation scripts for Fourier Neural Operators (FNOs)
• MATLAB data generation routines for EIT forward problems
• Data processing and plotting utilities
• An implementation of the regularized D-bar EIT reconstruction method

The FNO code defaults to running on GPU, if one is available.

Installation

The command

conda env create -f Project.yml

creates an environment called eit. PyTorch will be installed in this step.

Activate the environment with

conda activate eit

and deactivate with

conda deactivate

Data

The three datasets in the paper may be downloaded at https://doi.org/10.7298/fn0q-v573. There are three compressed directories:

• shape.zip: dataset for shape detection; 2.3 GB
• three_phase.zip: dataset for three-phase inclusions; 2.3 GB
• lognormal.zip: dataset for lognormal conductivities; 3.5 GB

Each file contains several Pytorch .pt data files as follows:

• OOD/: 6 out-of-distribution (OOD) test examples for evaluating model generalization beyond the training distribution
• conductivity.pt: a Pytorch dictionary with:
  • key conductivity
  • value a (10000, 256, 256) tensor; 2.6 GB
  • data type: single precision float torch.tensor (float32)
• conductivity_3heart_rhop7.pt: a Pytorch dictionary with:
  • key conductivity_3heart
  • value a (3, 256, 256) tensor
  • dtype: single precision float torch.tensor (float32)
• kernel.pt: a Pytorch dictionary with:
  • key kernel
  • value a (10000, 256, 256) tensor; 2.6 GB
  • dtype: single precision float torch.tensor (float32)
• kernel_3heart_rhop7.pt: a Pytorch dictionary with
  • key kernel_3heart
  • value a (3, 256, 256) tensor
  • dtype: single precision float torch.tensor (float32)
• mask.pt: a Pytorch dictionary with:
  • key mask
  • value a (256, 256) tensor
  • dtype: single precision float torch.tensor (float32)

For most users, it is enough to work with kernel.pt as model input (Neumann-to-Dirichlet integral kernel function) and conductivity.pt as model output (electrical conductivity). All data are original, raw, unnormalized field quantities.

If you use these data, please cite:

Nelsen, Nicholas H. (2025). Data from: Extension and neural operator approximation of the electrical impedance tomography inverse map [dataset]. Cornell University Library eCommons Repository. https://doi.org/10.7298/fn0q-v573.

You may also generate your own data in MATLAB (this will take over one day of wall-clock time). The requirements are:

• MATLAB R2019b
• Partial Differential Equation Toolbox
• Image Processing Toolbox

Citing

If you use learning-eit in an academic paper, please cite the main reference "Extension and neural operator approximation of the electrical impedance tomography inverse map" as follows:

@article{de2025extension,
  title={Extension and neural operator approximation of the electrical impedance tomography inverse map},
  author={{de Hoop}, Maarten V and Kovachki, Nikola B and Lassas, Matti and Nelsen, Nicholas H},
  journal={preprint arXiv:2511.20361},
  year={2025}
}

Other References

• Fourier Neural Operator for Parametric Partial Differential Equations
• Linear and Nonlinear Inverse Problems with Practical Applications
• Operator learning meets inverse problems: A probabilistic perspective
• An operator learning perspective on parameter-to-observable maps

Contribute

You are welcome to submit an issue for any questions related to learning-eit or to contribute to the code by submitting pull requests.

Acknowledgements

The FNO implementation in learning-eit is adapted from the original implementation by Nikola Kovachki and Zongyi Li and its modifications in fourier-neural-mappings. The data generation code and regularized D-bar solver are adapted from the publicly available code for the book Linear and Nonlinear Inverse Problems with Practical Applications by Jennifer L. Mueller and Samuli Siltanen. The matplotlib formatting used to produce figures is adapted from the PyApprox package by John Jakeman. Data curation assistance from the Cornell University Library is gratefully acknowledged.