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 (including some high-dimensional problems) and two finite element 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.

虽然多保真建模提供了一种成本效益高的方法来使用计算成本高的模型进行不确定性量化，但通过自适应地决定所需的高保真 (HF) 模拟的数量，可以实现更高的效率，具体取决于问题的类型和复杂性以及期望的结果准确性。我们提出了一个具有多保真建模的主动学习框架，强调对罕见事件的有效估计。我们的框架通过将低保真 (LF) 预测与 HF 推断校正融合在一起，过滤校正后的 LF 预测以决定是否调用高保真模型，并为提高后续准确性，在之后调整 LF 预测的校正每个 HF 模型调用。该框架不对 LF 模型类型或其与 HF 模型的相关性做出任何假设。此外，为了在估计较小的故障概率时提高鲁棒性，我们建议使用动态主动学习函数来决定何时调用 HF 模型。我们使用几个学术案例研究（包括一些高维问题）和两个有限元模型案例研究来展示我们的框架：使用斯托克斯近似估计 Navier-Stokes 速度和估计横向各向同性模型中的应力，这些模型通过粗网格各向同性受到位移模型。在这些案例研究中，所提出的框架不仅准确地估计了故障概率，而且与蒙特卡罗或标准方差减少方法相比，