An exact rescaling velocity method for some kinetic flocking models (Q2796856)

The authors provide extended analyses and interpretations of the parametrized-background data-weak (PBDW) formulation, a real-time in situ data assimilation framework for physical systems modeled by parametrized partial differential equations. First, the authors provide a brief overview of the PBDW formulation and provide an a priori error analysis in the presence of observation imperfections. Specifically, the authors consider observation noise which is zero-mean, homoscedastic, and uncorrelated; they provide an a priori error bound for the variance of the state estimation error. Then the authors provide a detailed interpretation of the PBDW data assimilation results obtained for a particular physical system: a raised-box acoustic resonator. Specifically, the authors analyze two different configurations of the system: a first configuration for which the dominant dynamics of the physical system is well anticipated, the dynamics is captured by the best-knowledge model, and the modeling error is small; a second configuration for which the dominant dynamics of the physical system is poorly anticipated, the dynamics is absent from the best-knowledge model, and the modeling error is large. Finally, the authors provide a strategy to update the PBDW based on an empirical representation of unmodeled physics obtained through data assimilation for a select few configurations. The strategy improves the experimental efficiency of the data assimilation procedure for all configurations of interest, and is particularly suited in many query scenarios which illustrate the approach for the raised-box acoustic resonator.