In the framework of reduced basis methods, we recently introduced a new certified hierarchical and adaptive surrogate model, which can be used for efficient approximation of input-output maps that are governed by parametrized partial differential equations. This adaptive approach combines a full order model, a reduced order model and a machine-learning model. In this contribution, we extend the approach by leveraging novel kernel models for the machine learning part, especially structured deep kernel networks as well as two layered kernel models. We demonstrate the usability of those enhanced kernel models for the RB-ML-ROM surrogate modeling chain and highlight their benefits in numerical experiments.

翻译：在约化基方法框架下，我们近期提出了一种新型认证分层自适应代理模型，可用于高效逼近由参数化偏微分方程控制的输入-输出映射。该自适应方法结合了全阶模型、约化阶模型与机器学习模型。本文通过引入新型核模型（特别是结构化深度核网络及双层核模型）用于机器学习部分，对该方法进行了拓展。我们论证了这些增强型核模型在RB-ML-ROM代理建模链中的可用性，并通过数值实验凸显其优势。