Linear Embedding-Enhanced Co-Kriging Incorporating Distinct Projection Matrices Across Fidelity Levels

Abstract

Abstract. Multi-fidelity (MF) modeling methods have been widely investigated for their ability to reduce the high computational costs of high-fidelity (HF) analyses by fusing data from different fidelity levels. Most existing MF approaches assume that the same low-fidelity (LF) embedding function can be applied to both LF and HF data, which is often violated in real-world problems. As a result, HF-specific response behavior is ignored, which can degrade model accuracy by referencing inappropriate LF points when predicting HF responses. To address this issue, this article proposes a linear embedding-enhanced co-Kriging (LECOK) method that incorporates distinct linear embedding functions for LF and HF data. LECOK constructs a covariance matrix that accounts for the difference in embedding functions by defining a kernel incorporating both embeddings. Furthermore, to mitigate the difficulty of accurately estimating the HF embedding function from limited HF samples, an optimization technique on the Stiefel manifold is employed using the proposed covariance matrix. By integrating these components, the proposed method extends the applicability of MF modeling by adapting to the level of similarity between the LF and HF embedding functions. This characteristic of the proposed method is demonstrated through both numerical and engineering examples.