We present an intuitive geometrical framework for non‐intrusive model reduction. Based on simple low‐dimensional geometry that is easy to visualize and interpret, the approach enables one to predict model features a priori and explain them a posteriori. Two simple a priori methods for analyzing the suitability of non‐intrusive model reduction are consequently presented and discussed. As a natural consequence of the interpretation proposed a method extension is proposed, namely, higher‐order temporal discretization. It is also demonstrated that some generic properties of the physical system modeled such as periodicity or convergence towards a steady state are easily represented in the framework proposed. The approaches are illustrated using a number of representative test problems including a three‐dimensional case of the Saffman–Taylor instability and an example exhibiting a propagating discontinuity. It is shown that this property makes the underlying non‐intrusive reduced order modeling nonsmooth meaning it will provide a poor representation of the system dynamics.

中文翻译：

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非侵入式降阶建模：几何框架，高阶模型和适用性的先验分析

我们提出了一种用于非侵入式模型简化的直观几何框架。该方法基于易于可视化和解释的简单低维几何，因此可以先验地预测模型特征并对其进行后验解释。因此，提出并讨论了两种简单的先验方法来分析非侵入式模型约简的适用性。作为提出的解释的自然结果，提出了一种方法扩展，即高阶时间离散化。还证明了所提出的框架中很容易表示出所建模的物理系统的某些通用属性，例如周期性或向稳态收敛。通过一系列具有代表性的测试问题来说明这些方法，其中包括Saffman-Taylor不稳定性的三维情况以及一个表现出传播不连续性的示例。结果表明，该属性使基础的非侵入式降阶建模不平滑，这意味着它将无法很好地表示系统动力学。