Parameter estimation in non linear mixed effects models requires a large number of evaluations of the model to study. For ordinary differential equations, the overall computation time remains reasonable. However when the model itself is complex (for instance when it is a set of partial differential equations) it may be time consuming to evaluate it for a single set of parameters. The procedures of population parametrization (for instance using SAEM algorithms) are then very long and in some cases impossible to do within a reasonable time. We propose here a very simple methodology which may accelerate population parametrization of complex models, including partial differential equations models. We illustrate our method on the classical KPP equation.
Mots-clés : parameter estimation, SAEM algorithm, partial differential equations, KPP equation
@article{M2AN_2014__48_5_1303_0,
author = {Grenier, E. and Louvet, V. and Vigneaux, P.},
title = {Parameter estimation in non-linear mixed effects models with {SAEM} algorithm: extension from {ODE} to {PDE}},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1303--1329},
publisher = {EDP-Sciences},
volume = {48},
number = {5},
year = {2014},
doi = {10.1051/m2an/2013140},
mrnumber = {3264355},
zbl = {1301.35177},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2013140/}
}
TY - JOUR AU - Grenier, E. AU - Louvet, V. AU - Vigneaux, P. TI - Parameter estimation in non-linear mixed effects models with SAEM algorithm: extension from ODE to PDE JO - ESAIM: Mathematical Modelling and Numerical Analysis PY - 2014 SP - 1303 EP - 1329 VL - 48 IS - 5 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2013140/ DO - 10.1051/m2an/2013140 LA - en ID - M2AN_2014__48_5_1303_0 ER -
%0 Journal Article %A Grenier, E. %A Louvet, V. %A Vigneaux, P. %T Parameter estimation in non-linear mixed effects models with SAEM algorithm: extension from ODE to PDE %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2014 %P 1303-1329 %V 48 %N 5 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2013140/ %R 10.1051/m2an/2013140 %G en %F M2AN_2014__48_5_1303_0
Grenier, E.; Louvet, V.; Vigneaux, P. Parameter estimation in non-linear mixed effects models with SAEM algorithm: extension from ODE to PDE. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 48 (2014) no. 5, pp. 1303-1329. doi : 10.1051/m2an/2013140. http://www.numdam.org/articles/10.1051/m2an/2013140/
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