Multifidelity Modeling Based on Numerical Eigenfunction Expansions

In this work, a novel method for constructing low-fidelity models tailored for eigenanalysis-based multi-fidelity surrogate optimization frameworks is proposed. Namely, the proposed approach leverages reference eigenfunction expansions to solve a properly formulated boundary value problem (BVP), enabling the rapid computation of characteristic mode solutions for arbitrary structures. To ensure uniqueness and well-posedness of the BVP, a computationally efficient two-dimensional Method of Moments (MoM) solution is employed to define the necessary boundary conditions. The resulting low-fidelity solutions are incorporated into a multi-fidelity surrogate modeling scheme by combining them with data from high-fidelity simulations. To enable consistent training and improve convergence, the characteristic mode solutions are organized through a robust correlation-based matching scheme. The proposed method is validated through two multi-objective characteristic mode analyses of microstrip patch antennas. Notably, our results demonstrate that the eigenfunction-based low-fidelity model yields solutions over three orders of magnitude faster than state-of-the-art coarse-mesh-based low-fidelity approaches. This acceleration translates to an approximate twofold reduction in total training time for multi-fidelity surrogate model, compared to conventional multi-fidelity strategies.