This work aims at studying specific ways of solving parameter identification problems, especially when these parameters depend on space and/or time. Firstly, a strategy using an adjoint state formulation is proposed to achieve the parameter identification of models described by ODEs. Different regularization strategies are proposed for specific cases of study, validating the choices made in the strategy. Secondly, the identification of spatial fields of properties is dealt with, for models described by PDEs. To solve such inverse problems, full-field measurements are crucial to get as much experimental information as possible. Then the strategy described before is improved by the use of a specific mesh for the spatial discretization of the parameter field: this mesh, initially coarse, is progressively refined according to mesh adaption techniques. This iterative strategy provides additional regularization properties, which improve the identification process, and which could tend to be multiscale. Thirdly, a truly multiscale identification process is proposed in the framework of periodic time homogenization. This latter method allows to efficiently describe the 'slow' variations of a system withstanding 'fast' cyclic loads. Some investigations are proposed on the associated multiscale parameter identification process.
