A Generalized Empirical Interpolation Method: application of reduced basis techniques to data assimilation
For researchers in computational science and engineering, it provides a framework to incorporate noisy observational data into PDE-based models, though the novelty is incremental.
The paper generalizes the empirical interpolation method and reduced basis method to integrate data mining and data assimilation, enabling reconstruction of noisy data for input into PDE models. It combines data acquisition with domain decomposition and reduced basis approximations.
This paper introduces a generalization of the empirical interpolation method (EIM) and the reduced basis method (RBM) in order to allow their combination with data mining and data assimilation. The purpose is to be able to derive sound information from data and reconstruct information, possibly taking into account noise in the acquisition, that can serve as an input to models expressed by partial differential equations. The approach combines data acquisition (with noise) with domain decomposition techniques and reduced basis approximations.