Data-driven discovery of canonical models in undergraduate differential equations education

Authors

• Devon L. Garls, Colorado School of MinesFollow
• Raina Majumder, Colorado School of MinesFollow
• Scott A. Strong, Colorado School of MinesFollow

Publication Date

10-27-2026

Keywords

SINDy, sparse regression, data-driven discovery, ordinary differential equa- tions, undergraduate mathematics education

Disciplines

Mathematics | Physical Sciences and Mathematics | Science and Mathematics Education

Abstract

Roughly a decade ago, Brunton, Proctor, and Kutz built upon the re-

sults of classical control theory, compressed sensing, and symbolic regression

to create a method for Sparse Identification of Nonlinear Dynamics (SINDy),

allowing one to infer a dynamical system from time series and bring mathe-

matical dynamics into the modern era of large data. This paper is designed for

a reader concurrently enrolled in a first course in ordinary differential equa-

tions and begins with a technical overview of least-squares regression and

finite-difference approximations to derivatives, which is enough to perform

an example hand-calculation on three data points. The SINDy package gener-

alizes this, which we illustrate with four canonical models of the introductory

curriculum, i.e., population, temperature, oscillatory, and mixing dynamics,

against public, experimental, and synthetic records. Resolving each requires

an increasing number of SINDy built-in utilities, i.e., sequential threshold-

ing, normalization of the feature library, and a ridge penalty swept over a

hyperparameter grid and resolved by cross-validation on a held-out state,

demonstrating model selection from the data rather than from contextual

assumptions. We conclude by outlining possible future work before transi-

tioning to a section dedicated to reproducing our results through a public

repository and to learning outcomes, with hand calculations, computational

exercises, and scaffolded projects collected in the Supplemental Materials, so

that SINDy can be utilized at a variety of levels of undergraduate education.

Recommended Citation

Garls, Devon L.; Majumder, Raina; and Strong, Scott A. (2026) "Data-driven discovery of canonical models in undergraduate differential equations education," CODEE Journal: Vol. 20: Iss. 2, Article 12.
Available at: https://scholarship.claremont.edu/codee/vol20/iss2/12

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