Machine Learning for Modeling in an Elementary Differential Equations Class

Authors

• Nathan Albin, Kansas State UniversityFollow
• Andrew G. Bennett, Kansas State UniversityFollow
• Abhinav Chand, University of Wisconsin - Eau ClaireFollow

Publication Date

5-19-2026

Keywords

Machine Learning, Spring, Python, Jupyter Notebook, non-linear damping

Disciplines

Mathematics | Ordinary Differential Equations and Applied Dynamics | Physical Sciences and Mathematics | Science and Mathematics Education

Abstract

Mixing machine learning with modeling is an area of increasing importance. This paper presents a lesson where students model a spring-mass system both using traditional analysis with linear damping and using machine learning to learn the damping from real data. The machine learning is implemented in a Jupyter notebook hosted on Google Colab, allowing students to train the neural network without requiring the students to carry out coding. Students get experience with how machine learning can fail, how it can work, and the time and data requirements for machine learning to succeed, and are asked to apply this knowledge to deciding when machine learning will be an appropriate tool in other modeling contexts. Student reaction has been positive. Suggestions for adaptations and extensions of the lesson are provided at the end.

Recommended Citation

Albin, Nathan; Bennett, Andrew G.; and Chand, Abhinav (2026) "Machine Learning for Modeling in an Elementary Differential Equations Class," CODEE Journal: Vol. 20: Iss. 2, Article 1.
Available at: https://scholarship.claremont.edu/codee/vol20/iss2/1

Rights Information

© 2026 the Author(s)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.