Multi-Fidelity Category-Tree Gaussian Process Modeling with Many Categorical Combinations

Abstract

Mixed-input computer experiments with many categorical combinations and multiple fidelity levels arise routinely in engineering simulation (e.g., CPU thermal modeling). While qualitative–quantitative Gaussian processes can represent heterogeneous categorical effects and Kennedy–O’Hagan style autoregressive GPs can fuse low- and high-fidelity data, a direct coupling of these ideas becomes computationally prohibitive when the number of categorical combinations is large, because it requires estimating complex cross-correlation structures across all categories at each fidelity level.

This work proposes a scalable multi-fidelity extension of the category-tree Gaussian process (ctGP). The key assumption is that the categorical correlation structure is shared across fidelity levels, enabling pooling of low- and high-fidelity data to jointly estimate a single cross-correlation matrix. This shared matrix serves as a similarity metric to guide recursive partitioning of the categorical space into a category tree, grouping highly correlated categorical combinations together. After growing the full tree, a leave-one-out cross-validation pruning step selects an optimal subtree to avoid overfitting. Finally, multi-fidelity surrogate models are fit independently within the terminal leaves: a standard autoregressive GP is used for leaves containing a single categorical combination, while an integrated mixed-input autoregressive model is used for leaves containing multiple grouped combinations.

A simulation study based on a modified Borehole benchmark demonstrates the feasibility and predictive strength of the proposed divide-and-conquer strategy, achieving accurate high-fidelity prediction while maintaining tractable computation for many-category, multi-fidelity settings.

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