In this contribution we apply an adaptive model hierarchy, consisting of a full-order model, a reduced basis reduced order model, and a machine learning surrogate, to parametrized linear-quadratic optimal control problems. The involved reduced order models are constructed adaptively and are called in such a way that the model hierarchy returns an approximate solution of given accuracy for every parameter value. At the same time, the fastest model of the hierarchy is evaluated whenever possible and slower models are only queried if the faster ones are not sufficiently accurate. The performance of the model hierarchy is studied for a parametrized heat equation example with boundary value control.

翻译：本文提出一种由全阶模型、约化基约化模型和机器学习代理组成的自适应模型层级，用于求解参数化线性二次型最优控制问题。所涉及的约化模型通过自适应方式构建，并采用逐级调用的策略，使得模型层级能够针对每个参数值返回满足给定精度的近似解。同时，在可能的情况下优先使用层级中最快的模型，仅当快速模型精度不足时才调用较慢的模型。本文通过含边界值控制的参数化热方程算例，验证了该模型层级的性能。