Soft Magnetic Materials Models with ODEs

Summary

This repository contains the slides and code related to the following webinar:

• Soft Magnetic Materials and Ordinary Differential Equations
• From Linear Circuits to Neural Network Models
• IEEE MagNet Challenge Webinar - May 23 2025
• Thomas Guillod - Dartmouth College

This webinar focuses on ordinary differential equation models for soft-magnetic materials:

• Using equation-based models (linear and nonlinear circuits)
• Using neural ordinary differential equation models

The Python code has the following features:

• Training and inference of ODE models
• Management of the dataset with dataframes
• Various metrics and plotting capabilities
• Using JAX for computations (does not require a GPU)
• Using Diffrax for solving the ODEs (with adjoints)

Various optimizers can be used to train the models:

• Scipy / latin hypercube sampler
• Scipy / differential evolution
• JAX / Optimistix / minimize solver
• JAX / Optimistix / least-square
• JAX / Optax / gradient descent

Repository Description

• Main Files
  • slides.pdf - Slides of the webinar (CC BY-ND 4.0)
  • requirements.txt - List of the used Python packages.
• Python Files
  • run_1_dataset.py - Parse the CSV files into a DataFrame.
  • run_2_eqn_train.py - Train an equation-based model.
  • run_3_eqn_infer.py - Inference of an equation-based model.
  • run_4_ann_train.py - Train a neural network-based model.
  • run_5_ann_infer.py - Inference of a neural network-based model.
  • model_eqn.py - Specifications of the equation-based models.
  • model_ann.py - Specifications of the neural network-based models.
• Folders and Python Packages
  • data - Folder containing the datasets and trained models.
  • odemodel - Python package with the definition of the models.
  • odesolver - Python package with the training and inference code.

Disclaimers

• The goal of this code is to demonstrate basic ODE models.
• The implementation is neither comprehensive nor optimized.
• The dataset provided in the repository is very small.
• The dataset is extracted from the MagNetX dataset.

Compatibility

• Tested on Linux x86/64.
• Tested with Python 3.12.3.
• Package list in requirements.txt.

Author

• Name: Thomas Guillod
• Affiliation: Dartmouth College
• Email: [email protected]
• Website: https://otvam.ch

Credits

This research was done at Dartmouth College by the research group of Prof. Sullivan:

• Dartmouth College, NH, USA: https://dartmouth.edu
• Dartmouth Engineering: https://engineering.dartmouth.edu

Copyright

(c) 2024-2025 / Thomas Guillod / Dartmouth College

This Source Code Form is subject to the terms of the Mozilla Public License, v. 2.0. If a copy of the MPL was not distributed with this file, You can obtain one at http://mozilla.org/MPL/2.0/.