RSAL-iMFS: A framework of randomized stacking with active learning for incremental multi-fidelity surrogate modeling.

Multi-fidelity surrogate (MFS) modeling incorporates a large number of low-fidelity (LF) samples with a small size of high-fidelity (HF) samples to obtain accurate HF approximations of unknown inputs. Because they save costs when labeling massive HF samples, MFS modeling techniques have been widely used in many engineering problems such as rapid simulation and mechanism optimization. In this paper, we propose a framework of randomized stacking with active learning for incremental MFS modeling (RSAL-iMFS). The framework contains two parts: randomized stacking for incremental MFS modeling (RS-iMFS) and query-by-committee (QBC)-based active learning for MFS modeling (QBC-AL-MFS). In particular, we first randomly project the inputs of LF samples into different spaces spanned by random projection matrices to form new LF samples and build a series of LF regressors based on the transformed LF samples to capture the LF features from different views. Then, these base LF regressors are stacked to form the inputs of the subsequent incremental Gaussian process regression (iGPR) model for approximating the HF responses. To achieve improved modeling performance, we also adopt the QBC-based active learning (QBC-AL) method to recommend unlabeled inputs from the input pool of candidate HF samples according to their distances, which are weighted by using the divergence of the committee voting results. We then label these recommended inputs to incrementally update the current iGPR model. Numerical experiments validate the proposed framework in incremental MFS modeling tasks and show that (1) RSAL-iMFS outperforms the state-of-the-art models; (2) Gaussian projection matrices (GPMs) can be reasonable choices in most cases; and (3) RSAL-iMFS's modeling performance has low sensitivity to the choice of the number of base regressors.