Rebecca Morrison, Uni Colorado, will discuss: Highly reduced models of random ODEs: A framework, some examples, and analysis
Consider a modeler's job when tasked to describe a system of interacting species, such as compartmental models in epidemiology: in many cases, interaction coefficients are unknown, relevant data are unavailable, inclusion of all possible species is computationally infeasible, etc. Thus, the modeler will have to model the system with just a small subset of the active species. This would seem to make the modeler's job extremely difficult, or even perhaps a lost cause. Surprisingly, though, we have examined several cases of random nonlinear ordinary differential equations where this type of extreme reduction---along with a simple, data-driven, embedded enrichment operator---still results in descriptive and predictive models. In this talk, I'll review a framework for calibration and validation of these coupled systems, show a few specific numerical examples, and give some analysis that supports such reductions.
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