Active learning-assisted multi-fidelity surrogate modeling based on geometric transformation

Multi-fidelity data are common in various scientific and engineering fields. High-fidelity data, often more accurate, come with greater expense, such as precision experimental testing or high-resolution simulation. Conversely, low-fidelity data are less accurate but more cost-effective. Multi-fidelity surrogate modeling, which integrates multi-fidelity data to build a model, is widely used for its ability to reduce costs while improving modeling accuracy. In this work, we introduce an innovative method named active learning-assisted multi-fidelity surrogate modeling based on geometric transformation (AL-MFSGT). The AL-MFSGT method comprises three essential components: the two-fidelity surrogate based on geometric transformation (TFSGT), an active learning (AL) strategy, and a multi-fidelity modeling framework. TFSGT utilizes geometric transformations to adjust the low-fidelity surrogate to align it more closely with the high-fidelity data. Then, the transformed low-fidelity surrogate and the high-fidelity surrogate are coupled using correlation functions. The AL strategy combines accelerating error convergence and enhancing sample set diversity to judiciously select high-fidelity incremental samples. Subsequently, the two-fidelity surrogate modeling is extended to a comprehensive multi-fidelity framework. To validate the efficacy of AL-MFSGT, we conduct extensive comparative experiments using ten numerical examples. The results demonstrate the superiority of AL-MFSGT over several compared multi-fidelity surrogate modeling methods. Furthermore, we apply AL-MFSGT to two practical engineering cases, demonstrating its effectiveness in real-world modeling scenarios.