Parameter estimation in non-linear mixed effects models with SAEM algorithm: extension from ODE to PDE.

Emmanuel Grenier (1, 2) , Violaine Louvet (2, 3, 4) , Paul Vigneaux (1, 2)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
2 NUMED - Numerical Medicine
3 ICJ - Institut Camille Jordan
4 MMCS - Modélisation mathématique, calcul scientifique

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

Domaines: Analyse numérique [math.NA]; Statistiques [math.ST]; Théorie [stat.TH]; Equations aux dérivées partielles [math.AP]

Emmanuel Grenier, Violaine Louvet, Paul Vigneaux. Parameter estimation in non-linear mixed effects models with SAEM algorithm: extension from ODE to PDE.. ESAIM: Mathematical Modelling and Numerical Analysis, 2014, 48 (5), pp.1303-1329. ⟨10.1051/m2an/2013140⟩. ⟨hal-00936373v2⟩