A multi-output multi-fidelity Gaussian process model for non-hierarchical low-fidelity data fusion

摘要

Multi-fidelity (MF) surrogate model has been widely used in dealing with computationally expensive problems as it can make a trade-off between computational cost and modeling accuracy. Most existing MF models are under the assumption of a hierarchical relationship between different fidelity models. In other words, the fidelity level of each low-fidelity (LF) model can be clearly identified. However, the fidelity rankings of the LF models are indistinguishable in many practical problems. Hence, the existing MF models may be inapplicable when dealing with multiple non-hierarchical LF data. To address this issue, a multi-fidelity Gaussian process model for multiple non-hierarchical LF data fusion is developed in multi-output scenarios. It focuses on approximating multiple dependent high-fidelity (HF) responses assisted by multiple non-hierarchical LF data. The multi-output Gaussian process modeling technique makes the proposed model able to catch the latent correlations between outputs. In such a structure, both the information of the multiple LF data and the correlations between outputs can be fully exploited to further enhance the prediction accuracy. The effectiveness of the proposed model is tested using two analytical examples and a metamaterial vibration isolator design problem. It is shown that the proposed model gives the best predictions among the tested models for most cases. Results show that the proposed method can be a potential multi-output multi-fidelity modeling approach for computationally expensive problems in dealing with multiple non-hierarchical LF data.