[en] Differential equations (DEs) are commonly used to describe dynamic systems evolving in one (ordinary differential equations or ODEs) or in more than one dimensions (partial differential equations or PDEs). In real data applications the parameters involved in the DE models are usually unknown and need to be estimated from the available measurements together with the state function. In this paper, we present frequentist and Bayesian approaches for the joint estimation of the parameters and of the state functions involved in PDEs. We also propose two strategies to include differential (initial and/or boundary) conditions in the estimation procedure. We evaluate the performances of the proposed strategy on simulated and real data applications.
Disciplines :
Mathematics
Author, co-author :
Frasso, Gianluca ; Université de Liège - ULiège > Institut des sciences humaines et sociales > Méthodes quantitatives en sciences sociales
Jaeger, Jonathan ; Université de Liège - ULiège > Institut des sciences humaines et sociales > Méthodes quantitatives en sciences sociales
Lambert, Philippe ; Université de Liège - ULiège > Institut des sciences humaines et sociales > Méthodes quantitatives en sciences sociales
Language :
English
Title :
Estimation and approximation in multidimensional dynamics
Publication date :
22 November 2013
Number of pages :
17
Funders :
BELSPO - SPP Politique scientifique - Service Public Fédéral de Programmation Politique scientifique