Seminar 25.3.2021: Katarina Bodova
Posted: Sun Mar 14, 2021 1:47 amSeminár z kvalitatívnej teórie diferenciálnych rovníc
Seminar on Qualitative Theory of Differential Equations
Thursday 25.3.2021 at 14:00
Katarína Boďová (KMANM FMFI UK):
Dynamic maximum entropy approximation for understanding complex stochastic dynamics
MS-teams link:
https://teams.microsoft.com/l/meetup-jo ... afe3%22%7d
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:
(1) the approximation recovers the exact solution,
(2) the approximation is accurate but not exact,
(3) the approximation fails.
Seminar on Qualitative Theory of Differential Equations
Thursday 25.3.2021 at 14:00
Katarína Boďová (KMANM FMFI UK):
Dynamic maximum entropy approximation for understanding complex stochastic dynamics
MS-teams link:
https://teams.microsoft.com/l/meetup-jo ... afe3%22%7d
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:
(1) the approximation recovers the exact solution,
(2) the approximation is accurate but not exact,
(3) the approximation fails.