Advanced non-hierarchical co-Kriging using latent map multi-output Gaussian process

Abstract

To achieve the accuracy of high-fidelity models at a reduced computational cost, multi-fidelity modeling techniques have been developed to incorporate low-fidelity data into surrogate model construction. Among them, non-hierarchical multi-fidelity methods have gained attention due to their ability to construct multi-fidelity models without a prescribed hierarchy among multiple low-fidelity outputs. However, current non-hierarchical multi-fidelity methods face significant challenges in capturing complex correlations among low-fidelity sources and between high-fidelity and low-fidelity datasets; linear combination models often neglect inter-source dependencies, and latent variable-based approaches such as the latent map Gaussian process are limited by fixed low-dimensional latent spaces and the absence of discrepancy modeling for the high-fidelity response. These limitations hinder both accuracy and robustness, particularly in data-scarce settings. To address these issues, this paper proposes an advanced non-hierarchical multi-fidelity framework based on a latent map multi-output Gaussian process. The proposed method models low-fidelity correlations via multi-output Gaussian processes and captures relationships between high- and low-fidelity through co-Kriging, including an explicit discrepancy term. In latent map multi-output Gaussian process, a decomposition-based optimization scheme is introduced to estimate higher-dimensional latent coordinates, enhancing both model flexibility and robustness. Furthermore, low-fidelity weights are estimated from inter-fidelity correlations derived from the latent map multi-output Gaussian process, rather than being determined by conventional tuning criteria. Numerical and engineering examples demonstrate that the proposed method achieves superior accuracy and stability compared to existing non-hierarchical multi-fidelity approaches.