Comparison of Co-Kriging, Composite Neural Networks, and Kolmogorov Arnold Networks for Multi-Fidelity Surrogate Modeling

Multi-fidelity surrogate modeling (MFSM) is a powerful tool that creates a single mathematical model from two or more sets of data having disparate fidelities. Accurate high-fidelity data are typically expensive and sparse; low-fidelity data are less accurate, cheaper, and more available. Despite MFSM’s advantages, it is unclear which MFSM algorithm is most appropriate. This work seeks to partially address this problem by characterizing and comparing three MFSM algorithms: Co-Kriging (i.e., baseline MFSM algorithm), Composite Neural Networks, and Kolmogorov Arnold Networks. Each algorithm is tested on three analytical benchmark problems – continuous 1D, discontinuous 1D, and continuous 2D – demonstrating the effects of dimensionality and nonlinearity. Comparisons are made on each algorithm’s ability to capture complex model features, input vector dimensionality, and data set size. Results show deep learning methods can capture complex nonlinear and discontinuous datasets at an added expense of hyperparameter tuning.