论文标题
一个新的认证层次和自适应RB-ML-ROM替代模型，用于参数化PDE
A new certified hierarchical and adaptive RB-ML-ROM surrogate model for parametrized PDEs
论文作者
论文摘要
我们提出了一种新的替代建模技术，用于有效近似由参数化PDE的输入输出图。该模型是层次结构的，因为它是在完整订单模型（FOM），减少订单模型（ROM）和机器学习（ML）模型链上构建的。该模型是自适应的，从某种意义上说，在对模型的一系列参数请求过程中，ROM和ML模型是在正式中进行调整的。为了允许对模型层次结构进行认证以及控制适应过程，我们对ROM和ML模型进行了严格的后验错误估计。特别是，我们提供了一个基于ML的模型的示例，该模型允许进行严格的分析质量语句。我们证明了建模链在蒙特卡洛和参数优化示例上的效率。在这里，ROM是通过减少基础方法实例化的，ML模型由神经网络或VKOGA内核模型给出。
We present a new surrogate modeling technique for efficient approximation of input-output maps governed by parametrized PDEs. The model is hierarchical as it is built on a full order model (FOM), reduced order model (ROM) and machine-learning (ML) model chain. The model is adaptive in the sense that the ROM and ML model are adapted on-the-fly during a sequence of parametric requests to the model. To allow for a certification of the model hierarchy, as well as to control the adaptation process, we employ rigorous a posteriori error estimates for the ROM and ML models. In particular, we provide an example of an ML-based model that allows for rigorous analytical quality statements. We demonstrate the efficiency of the modeling chain on a Monte Carlo and a parameter-optimization example. Here, the ROM is instantiated by Reduced Basis Methods and the ML model is given by a neural network or a VKOGA kernel model.
