Seminar on Qualitative Theory of Differential Equations - Katarína Boďová (25.3.2021)
Thursday 25.3.2021 at 14:00, online
Katarína Boďová:
Dynamic maximum entropy approximation for understanding complex stochastic dynamics
Abstract:
Realistic models of biological processes typically involve interacting components on multiple scales, driven by changing environment and inherent stochasticity. Such models are often analytically and numerically intractable. I will present a dynamic maximum entropy (DME) method, which approximates the full dynamics by a low-dimensional system of ODEs describing the system. The method circumvents the problem of closing an infinite hierarchy of moment equations by choosing a suitable set of functions, whose averages are followed in time. Using a quasi-stationarity assumption, the problem reduces to low-dimensional dynamics, which show great accuracy even in non-stationary problems. While estimating accuracy of the method is still an open problem, I will present a couple of applications ranging in complexity where:
- the approximation recovers the exact solution,
- the approximation is accurate but not exact,
- the approximation fails.