A Generalized Empirical Interpolation Method: application of reduced basis techniques to data assimilation

TL;DR

This paper presents a generalized empirical interpolation method that combines reduced basis techniques with data assimilation, enabling robust data-driven modeling and reconstruction from noisy data for PDE-based systems.

Contribution

It introduces a unified framework integrating EIM, RBM, and data assimilation, enhancing data-driven model reduction and reconstruction capabilities.

Findings

Effective handling of noisy data in model reconstruction

Improved accuracy in data assimilation with reduced basis methods

Framework applicable to PDE-based modeling

Abstract

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.