High-fidelity (HF) samples are accurate but are obtained at high cost. In contrast,low-fidelity (LF)samples are widely available but provide rough approximations. Multi-fidelity modeling aims to incorporate massive LF samples with a small amount of HF samples to develop a model for accurately approximating the HF responses to unseen inputs.In the literature,a main body of MFS models, under the assumption that there is a linear-trend relation between LF and HF data, are derived from the interpolation methods including the radial basis function method,the kriging method and the polynomial response surface (PRS) method. However,the linear-trend assumption will not always hold in practice, and thus the interpolation-based MFS models usually have a limited generality.Instead, some machine-learning methods (such as feed forward neural network and support vector regression) were used to handle MFS modeling tasks regardless of the relatedness between HF and LF data. Nevertheless,when the HF samples are rarely few, the training of machine-learning based MFS models is still challenged because the number of undetermined parameters is usually smaller than the HF-sample size.In this study, we propose two new machine-learning based MFS models: the hierarchical regression framework and the generative adversarial network. Compared with the classical MFS models,the two models have a better performance with a lower demand on HF-sample size and meanwhile without any assumption on the relation between HF and LF data. |
