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

Abstract

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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.

How to cite

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Frederix, 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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