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Soft Magnetic Materials and Ordinary Differential Equations: From Linear Circuits to Neural Network Models

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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

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

Credits

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

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/.

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Soft Magnetic Materials and Ordinary Differential Equations: From Linear Circuits to Neural Network Models

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