A professional development course on data-driven dynamical systems at a primarily undergraduate institution: Part A - Scientific Content

Authors

• Alessandro M. Selvitella, Department of Mathematical Sciences, Purdue University Fort WayneFollow
• Jeffrey R. Anderson, Department of Mathematical Sciences, Purdue University Fort WayneFollow

Keywords

data-driven dynamical systems, professional development, graduate teaching assistants, physics-informed machine learning, primary undergraduate institutions

Disciplines

Data Science | Dynamic Systems | Mathematics | Non-linear Dynamics | Numerical Analysis and Computation | Ordinary Differential Equations and Applied Dynamics | Physical Sciences and Mathematics | Science and Mathematics Education

Abstract

In the age of data-driven decision making, ordinary differential equations (ODEs) remain a powerful and interpretable framework for modeling dynamic processes, especially when integrated with modern tools from statistical learning and data-driven dynamical systems. Yet, general undergraduate and graduate curricula do not typically address key opportunities in data-driven dynamical systems.

This first paper in a series focuses on the mathematical and methodological core of a professional development course first developed in the academic year 2025-2026 at a Primarily Undergraduate Institution, Purdue University Fort Wayne. The curriculum developed in this course emphasized how regression, regularization, and sparse identification can be used to connect ODE models with time series data in a way that is accessible to advanced undergraduates. Therefore, we present a coherent set of modules that review linear regression and regularization as a statistical foundation, show how ODEs can be treated as interpretable models fitted to data, and introduce modern data-driven dynamical systems techniques such as Dynamic Mode Decomposition (DMD) and Sparse Identification of Nonlinear Dynamics (SINDy) in stripped-down, classroom-ready forms. Detailed examples, including a fully worked van der Pol oscillator case study with executable Python code, illustrate how least squares, sparse modeling, and ODE analysis can be combined in practice.

The emphasis throughout is on mathematically rigorous yet pedagogically accessible treatment of core ideas, with explicit activities and code snippets designed for direct use in an undergraduate ODE course. This paper lays the groundwork for the companion papers in the series, which will address GTA professional development logistics, implementation at scale, and assessment of teaching and learning outcomes.

Recommended Citation

Selvitella, Alessandro M. and Anderson, Jeffrey R. (2026) "A professional development course on data-driven dynamical systems at a primarily undergraduate institution: Part A - Scientific Content," CODEE Journal: Vol. 20: Iss. 2, Article 3.
Available at: https://scholarship.claremont.edu/codee/vol20/iss2/3