Basic dynamical model as an instrument for retrieval of non-observable variables from data

Basic dynamical models (BDMs) of observed phenomenon are known an effective tool for investigation of dynamical properties of underlying system. BDM is a model describing dynamical processes with established time scale corresponding to investigated phenomenon; typically it is derived from the detailed model of the system including a full set of first-principals equations, by separation of “fast” and “slow” families of dynamic variables. As a result, “slow” families are assumed to be constant during the evolution, while “fast” ones are in the instantaneous equilibrium state which depends on model variables with considered time scale. Though this model has much smaller dimension than the “full” model, it (1) describes basic properties of system dynamics and (2) includes physically-based parameters and dynamic variables of studied system. These features allow us to consider BDMs as an instrument for extraction the information about non-observable characteristics of the system from data.