# An analysis of noise propagation in the multiscale simulation of coarse Fokker-Planck equations

Yves Frederix; Giovanni Samaey; Dirk Roose

ESAIM: Mathematical Modelling and Numerical Analysis (2011)

- Volume: 45, Issue: 3, page 541-561
- ISSN: 0764-583X

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topFrederix, Yves, Samaey, Giovanni, and Roose, Dirk. "An analysis of noise propagation in the multiscale simulation of coarse Fokker-Planck equations." ESAIM: Mathematical Modelling and Numerical Analysis 45.3 (2011): 541-561. <http://eudml.org/doc/197481>.

@article{Frederix2011,

abstract = {
We consider multiscale systems for which only a fine-scale
model describing the evolution of individuals (atoms,
molecules, bacteria, agents) is given, while we are interested in the
evolution of the population density on coarse space and time
scales. Typically, this evolution is described by a coarse
Fokker-Planck equation.
In this paper, we consider a numerical procedure to compute the solution of
this Fokker-Planck equation directly on the coarse level, based on the
estimation of the unknown parameters (drift and diffusion)
using only appropriately chosen realizations of the fine-scale,
individual-based
system. As these parameters might be space- and time-dependent, the
estimation is performed in every spatial discretization point and at
every time step. If the fine-scale model is stochastic, the estimation
procedure introduces noise on the coarse level.
We investigate stability conditions for this procedure in the
presence of this noise and present an
analysis of the propagation of the estimation error in the numerical
solution of the coarse Fokker-Planck equation.
},

author = {Frederix, Yves, Samaey, Giovanni, Roose, Dirk},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis},

keywords = {Multiscale computing; stochastic systems; Fokker-Planck
equation; uncertainty propagation; multiscale computing; Fokker-Planck equation},

language = {eng},

month = {1},

number = {3},

pages = {541-561},

publisher = {EDP Sciences},

title = {An analysis of noise propagation in the multiscale simulation of coarse Fokker-Planck equations},

url = {http://eudml.org/doc/197481},

volume = {45},

year = {2011},

}

TY - JOUR

AU - Frederix, Yves

AU - Samaey, Giovanni

AU - Roose, Dirk

TI - An analysis of noise propagation in the multiscale simulation of coarse Fokker-Planck equations

JO - ESAIM: Mathematical Modelling and Numerical Analysis

DA - 2011/1//

PB - EDP Sciences

VL - 45

IS - 3

SP - 541

EP - 561

AB -
We consider multiscale systems for which only a fine-scale
model describing the evolution of individuals (atoms,
molecules, bacteria, agents) is given, while we are interested in the
evolution of the population density on coarse space and time
scales. Typically, this evolution is described by a coarse
Fokker-Planck equation.
In this paper, we consider a numerical procedure to compute the solution of
this Fokker-Planck equation directly on the coarse level, based on the
estimation of the unknown parameters (drift and diffusion)
using only appropriately chosen realizations of the fine-scale,
individual-based
system. As these parameters might be space- and time-dependent, the
estimation is performed in every spatial discretization point and at
every time step. If the fine-scale model is stochastic, the estimation
procedure introduces noise on the coarse level.
We investigate stability conditions for this procedure in the
presence of this noise and present an
analysis of the propagation of the estimation error in the numerical
solution of the coarse Fokker-Planck equation.

LA - eng

KW - Multiscale computing; stochastic systems; Fokker-Planck
equation; uncertainty propagation; multiscale computing; Fokker-Planck equation

UR - http://eudml.org/doc/197481

ER -

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