EXPO 2026: "Model Competition and Law Discovery in Differential Equations"
Автор: SIMIODE
Загружено: 2026-03-04
Просмотров: 7
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Sat | 8:30 PM–9:00 PM ET
Tosh Shahrtash; Pennsylvania College of Technology, Williamsport, PA USA
Abstract: Recent advances in artificial intelligence make it possible to rethink how differential equations are introduced and understood in undergraduate mathematics and engineering courses. We propose a modeling-first paradigm in which differential equations are framed as empirically discoverable laws. AI serves not as a problem-solver, but as an enabling infrastructure that generates rich, physics-consistent datasets, virtual experiments, and alternative modeling scenarios that would not be feasible in traditional classroom settings.
Within this framework, students engage in activities such as law discovery from large datasets, model competition, and maker-finder exchanges in which students both generate and identify governing equations. Python is used to estimate rates, visualize structure, and compare candidate models, while human judgment remains central in interpreting evidence, selecting appropriate laws, and articulating assumptions. Mathematical theory and solution techniques are intentionally delayed until after a governing law has been established, reframing analytic methods as tools for validation and prediction rather than endpoints.
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