Seminar on Qualitative Theory of Differential Equations - Fleur Slegers (23.4.2026)

Thursday 23.4.2026 at 14:00, Lecture room M 223

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Fleur Slegers:
Comparing Dynamic Maximum Entropy Methods for Multiscale Population Dynamics

Abstract: 
Dimension-reduction methods are valuable tools for analyzing complex stochastic systems, as they capture essential macroscopic dynamics without requiring full resolution of microscopic degrees of freedom.
This talk summarizes progress made during the two-month research visit at FMFI UK, focused on comparison of two such approaches: Dynamic Maximum Entropy (DME) and Dynamic MaxEnt across Entwined Scales (DyMES). Both methods approximate the system state by a maximum-entropy probability distribution constrained by a small set of macroscopic observables and derive evolution equations for these observables.
They differ, however, in the choice of observables and in the formulation of the reduced dynamics. DyMES was introduced specifically for scale-entwined systems, in which microscale dynamics depend on macroscale quantities, but its validity has not yet been systematically assessed. We test both methods on the Ornstein–Uhlenbeck process and on a stochastic multi-species population model with migration.
Our results show that DME remains applicable in scale-entwined settings, whereas assumptions underlying DyMES can lead to incorrect predictions.

This is joint work with Katarína Boďová.

 

 

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