Structured Learning for Electromagnetic Field Modeling and Real-Time Inversion

Overview of the OctoMag and Navion datasets.

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This repository contains the code accompanying the paper “Structured Learning for Electromagnetic Field Modeling and Real-Time Inversion”. In this repo you will find:

• The collected datasets for the OctoMag and Navion Electromagnetic Navigation Systems (eMNS),
• Implementations of the proposed structured learning-based models as well as the benchmark black-box models,
• Trained parameters for all models considered in the paper,
• Notebooks for data processing as well as model training and evaluation.

Citation

If you use this repository in your research, please cite the accompanying paper:

@article{Bernardes2026StructuredLearning,
  author  = {Bernardes, Antonio and Zughaibi, Jasan and Muehlebach, Michael and Nelson, Bradley J.},
  title   = {Structured Learning for Electromagnetic Field Modeling and Real-Time Inversion},
  journal = {arXiv preprint arXiv:2602.06618},
  year    = {2026},
  url     = {https://arxiv.org/abs/2602.06618}
}

Installation

Requirements

• Python 3.8.x (this codebase is tested/supported on Python 3.8)

Create and activate a Python 3.8 virtual environment, then install dependencies. On a Linux machine:

python3.8 --version  # should print 3.8.x

python3.8 -m venv magcalibration
source magcalibration/bin/activate

pip install -r requirements.txt

Datasets

The datasets are included in this repository under data/:

data/
└── octomag_data/
    └── data/              # OctoMag dataset
└── navion_data/
    └── data/              # Navion dataset

You can visualize the datasets using:

notebooks/
├── visualize_octomag.ipynb                 # OctoMag dataset
└── visualize_navion.ipynb                  # Navion dataset

Models

This repository contains implementations and trained parameters for the learning-based models and an interface for the MPEM baseline.

Model interface

In notebooks/usage_example.ipynb you will find a quick demonstration of how to use the considered models through an unified interface.

Learning-based models

All learning-based model code lives in:

• Implementation: src/calibration/

Trained parameters for learning-based models:

• Neural models: notebooks/training/octomag_params/ or notebooks/training/navion_params/
• Gradient-boosted linear tree regressor: notebooks/training/octomag_trees/ or notebooks/training/navion_trees/

MPEM baseline

For the MPEM (Multipole Expansion Model), the open source implementation is found in:

https://github.com/ethz-msrl/Tesla_core/tree/master/mag_control/mpem

And as a Python package (available only for x86 architecture):

https://pypi.org/project/mag-manip/

The optimized parameters are found in mpem/.

Workflow

1. Data processing

The notebooks in notebooks/processing/ cover the full preprocessing pipeline:

1. outliers_in_currents.ipynb
   Applies RANSAC-based outlier removal.

2. split_dataset.ipynb
   Splits the cleaned dataset into train/validation/test sets.

3. downsample.ipynb
   Downsamples the train and validation sets for the data-resolution ablation experiments. In the paper, this is performed only for the OctoMag dataset, with reductions to 50%, 20%, 5%, and 1%.

The notebooks should be run in the order defined in the list above.

2. Model training

Each model type has a dedicated training notebook:

1. train_nn.ipynb For training neural models.

2. train_gbt.ipynb For training gradient-boosted linear-tree regressors.

3. train_mpem.ipynb For training MPEM models. Note that this requires a ROS installation and the framework in:

https://github.com/ethz-msrl/Tesla_core/tree/master/mag_control/mpem

Training with your own dataset

The training (and evaluation) pipelines expect a pickled pandas.DataFrame with the following columns:

• Position: x, y, z
  Cartesian coordinates where the magnetic field was measured.
• Magnetic field: Bx, By, Bz
  Measured field vector components at that position.
• Coil currents: em_*
  One column per coil. For example, em_1, em_2, em_3, in a 3-coil system.

Training with the provided datasets

After running steps 1. and 2. of the data-processing pipeline above, the directory data/octomag_data/split_dataset/ or data/navion_data/split_dataset/ will contain pickled train/validation/test splits of the cleaned dataset of the corresponding eMNS, ready to be used by the training notebooks.

3. Model evaluation

To avoid recomputing each model’s magnetic field and gradient predictions for each test/plot, we use the EvaluationPackage class (defined in src/evaluate/) which stores predictions for a chosen set of models and provides utilities for downstream evaluation.

Step 1 — Assemble/cached predictions
Run notebooks/testing/assemble_data.ipynb to build an EvaluationPackage.
This notebook is already configured with the set of models evaluated in the paper.

NOTE: This notebook assumes the required downsampled training and validation sets already exist. Therefore, before running it, complete Step 3. (downsample.ipynb) in the data-processing pipeline above for the 50%, 20%, 5%, and 1% reduction settings.

Step 2 — Use the cached package
Once assembled, the EvaluationPackage can be loaded by the notebooks in:

• notebooks/testing/ for quick checks and comparisons
• notebooks/paper_plots/ to reproduce the figures reported in the paper

4. MPEM workspace analysis (Navion)

The workspace conditioning analysis was conducted using the notebooks in notebooks/workspace_analysis/:

1. divide_workspace.ipynb Divides data into cylindrical (or rectangular) segments.
2. workspace_analysis.ipynb Runs the workspace analysis required for the plotting in notebooks/paper_plots/workspace.ipynb