Parameter estimation in non-linear mixed effects models with SAEM algorithm: extension from ODE to PDE
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 5, p. 1303-1329
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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.

DOI : https://doi.org/10.1051/m2an/2013140
Classification:  35Q62,  35Q92,  35R30,  65C40,  35K57
Keywords: parameter estimation, SAEM algorithm, partial differential equations, KPP equation
@article{M2AN_2014__48_5_1303_0,
     author = {Grenier, Emmanuel 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 - Mod\'elisation Math\'ematique et Analyse Num\'erique},
     publisher = {EDP-Sciences},
     volume = {48},
     number = {5},
     year = {2014},
     pages = {1303-1329},
     doi = {10.1051/m2an/2013140},
     zbl = {1301.35177},
     mrnumber = {3264355},
     language = {en},
     url = {http://www.numdam.org/item/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 - Modélisation Mathématique et Analyse Numérique, Volume 48 (2014) no. 5, pp. 1303-1329. doi : 10.1051/m2an/2013140. http://www.numdam.org/item/M2AN_2014__48_5_1303_0/

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