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Differential equations (DEs) are commonly used to describe dynamic systemsevolving in one (ordinary differential equations or ODEs) or in more than onedimensions (partial differential equations or PDEs). In real data applicationsthe parameters involved in the DE models are usually unknown and need to beestimated from the available measurements together with the state function. Inthis paper, we present frequentist and Bayesian approaches for the jointestimation of the parameters and of the state functions involved in PDEs. Wealso propose two strategies to include differential (initial and/or boundary)conditions in the estimation procedure. We evaluate the performances of theproposed strategy on simulated and real data applications.

Estimation and approximation in multidimensional dynamics