PINNLab: An Interactive Dashboard for Teaching Data-Driven Parameter Estimation in Differential Equations using Physics-Informed Neural Networks

Authors

• Mohan J. Parthasarathy, Thomas Jefferson High School for Science and TechnologyFollow
• Padmanabhan Seshaiyer, George Mason UniversityFollow

Publication Date

6-16-2026

Keywords

Physics-Informed Neural Networks, Differential Equations, Parameter Estimation, Data-Driven Modeling

Disciplines

Applied Mathematics | Data Science | Numerical Analysis and Computation | Ordinary Differential Equations and Applied Dynamics | Science and Mathematics Education

Abstract

Undergraduate instruction in ordinary differential equations (ODEs) is typically organized around the forward problem: finding solution trajectories when the governing equation and its parameters are known. In scientific practice, however, inverse problems are often more relevant, requiring unknown parameters to be inferred from noisy observations while assessing whether a proposed model is consistent with the data. We introduce PINNLab, an open-source MATLAB dashboard designed to help undergraduate students explore inverse modeling through physics-informed neural networks (PINNs). PINNLab presents PINNs as a complementary data-driven framework that connects differential equations, optimization, empirical data, and scientific machine learning. The instructional sequence is organized around the 5E learning model and a T-shaped curricular framework. Students progress from qualitative ecological observation to synthetic-data parameter recovery and ultimately to comparative model evaluation using the historical Hudson's Bay Company hare--lynx trapping records. In the final module, students fit both the classical Lotka--Volterra system and an extended Holling Type II model, using data-fit and physics-based diagnostics to evaluate competing ecological explanations. Throughout the curriculum, PINNLab makes the modeling process visible through real-time visualization of state reconstruction, parameter convergence, configurable initial guesses, and loss diagnostics. By emphasizing the distinction between data fit and physical consistency, the platform encourages students to evaluate, critique, and revise mathematical models in the presence of noisy empirical observations. Students thereby learn to treat differential equations not merely as equations to be solved, but as testable hypotheses to be confronted with finite, noisy, and sometimes inconsistent empirical data.

Recommended Citation

Parthasarathy, Mohan J. and Seshaiyer, Padmanabhan (2026) "PINNLab: An Interactive Dashboard for Teaching Data-Driven Parameter Estimation in Differential Equations using Physics-Informed Neural Networks," CODEE Journal: Vol. 20: Iss. 2, Article 5.
Available at: https://scholarship.claremont.edu/codee/vol20/iss2/5