While multifidelity modeling provides a cost-effective way to conduct uncertainty quantification with computationally expensive models, much greater efficiency can be achieved by adaptively deciding the number of required high-fidelity (HF) simulations, depending on the type and complexity of the problem and the desired accuracy in the results. We propose a framework for active learning with multifidelity modeling emphasizing the efficient estimation of rare events. Our framework works by fusing a low-fidelity (LF) prediction with an HF-inferred correction, filtering the corrected LF prediction to decide whether to call the high-fidelity model, and for enhanced subsequent accuracy, adapting the correction for the LF prediction after every HF model call. The framework does not make any assumptions as to the LF model type or its correlations with the HF model. In addition, for improved robustness when estimating smaller failure probabilities, we propose using dynamic active learning functions that decide when to call the HF model. We demonstrate our framework using several academic case studies and two finite element (FE) model case studies: estimating Navier-Stokes velocities using the Stokes approximation and estimating stresses in a transversely isotropic model subjected to displacements via a coarsely meshed isotropic model. Across these case studies, not only did the proposed framework estimate the failure probabilities accurately, but compared with either Monte Carlo or a standard variance reduction method, it also required only a small fraction of the calls to the HF model.

翻译：虽然多种纤维模型提供了一种具有成本效益的方法,用成本昂贵的计算模型进行不确定性的量化,但根据问题的类型和复杂性以及预期结果的准确性,通过适应性决定所要求的高纤维(高频)模拟的数量,可以提高效率得多。我们提议了一个以多纤维模式积极学习的框架,强调对稀有事件的高效估计。我们的框架工作方式是用高频校正更正方式对低纤维(LF)预测进行低纤维(LF)预测,过滤经更正的低频预测,以决定是否调用高纤维模型,提高随后的准确性,在每次高频模型呼叫后调整对低频预测的更正。这个框架并不对低频模型类型或其与高频模型的相互关系作任何假设。此外,为了在估算较小的失败概率时提高稳健性,我们建议使用动态的积极学习功能决定何时调用高频模型。 我们仅使用若干学术案例研究和两个有限的要素来展示我们的框架:用不精确的数值估算纳维-斯托克(Navier-Stokos)标准框架,而是用不精确的方法对低位模型进行模拟估算。