Variants of the Empirical Interpolation Method: symmetric formulation, choice of norms and rectangular extension
For researchers using EIM in reduced-order modeling, this work offers theoretical generalizations and practical extensions, but the contributions are incremental.
The paper provides a symmetric formulation of the Empirical Interpolation Method (EIM), proves its existence and convergence for any norm, and introduces a rectangular extension to handle different numbers of selected values per variable, enabling sensor failure handling.
The Empirical Interpolation Method (EIM) is a greedy procedure that constructs approximate representations of two-variable functions in separated form. In its classical presentation, the two variables play a non-symmetric role. In this work, we give an equivalent definition of the EIM approximation, in which the two variables play symmetric roles. Then, we give a proof for the existence of this approximation, and extend it up to the convergence of the EIM, and for any norm chosen to compute the error in the greedy step. Finally, we introduce a way to compute a separated representation in the case where the number of selected values is different for each variable. In the case of a physical field measured by sensors, this is useful to discard a broken sensor while keeping the information provided by the associated selected field.