To efficiently tackle parametrized multi and/or large scale problems, we propose an adaptive localized model order reduction framework combining both local offline training and local online enrichment with localized error control. For the latter, we adapt the residual localization strategy introduced in [Buhr, Engwer, Ohlberger, Rave, SIAM J. Sci. Comput., 2017] which allows to derive a localized a posteriori error estimator that can be employed to adaptively enrich the reduced solution space locally where needed. Numerical experiments demonstrate the potential of the proposed approach.

翻译：为高效处理参数化多尺度和大规模问题，本文提出一种自适应局部化模型降阶框架，该框架结合局部离线训练与局部在线增广，并具备局部化误差控制能力。针对后者，我们改进了[Buhr, Engwer, Ohlberger, Rave, SIAM J. Sci. Comput., 2017]提出的残差局部化策略，该策略可推导出一种局部化后验误差估计子，用于在需要处自适应地局部增广降阶解空间。数值实验验证了所提方法的潜力。