This paper studies parametric reduced-order modeling via the interpolation of linear multiple-input multiple-output reduced-order, or, more general, surrogate models in the frequency domain. It shows that realization plays a central role and two methods based on different realizations are proposed. Interpolation of reduced-order models in the Loewner representation is equivalent to interpolating the corresponding frequency response functions. Interpolation of reduced-order models in the (real) pole-residue representation is equivalent to interpolating the positions and residues of the poles. The latter pole-matching approach proves to be more natural in approximating system dynamics. Numerical results demonstrate the high efficiency and wide applicability of the pole-matching method. It is shown to be efficient in interpolating surrogate models built by several different methods, including the balanced truncation method, the Krylov method, the Loewner framework, and a system identification method. It is even capable of interpolating a reduced-order model built by a projection-based method and a reduced-order model built by a data-driven method. Its other merits include low computational cost, small size of the parametric reduced-order model, relative insensitivity to the dimension of the parameter space, and capability of dealing with complicated parameter dependence.

中文翻译：

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通过异质替代物的插值对参数系统进行降阶建模

本文通过对线性多输入多输出降阶或更常用的替代频域内插模型进行插值研究参数化降阶建模。结果表明，实现起着核心作用，提出了两种基于不同实现的方法。用Loewner表示法对降阶模型进行插值等效于对相应的频率响应函数进行插值。在（实际）极点残差表示中插补降阶模型等效于对极点的位置和残差进行插值。事实证明，后一种极点匹配方法在逼近系统动力学方面更为自然。数值结果表明，极点匹配方法具有较高的效率和广泛的适用性。它显示了对由几种不同方法构建的代理模型进行插值的有效方法，这些方法包括平衡截断方法，Krylov方法，Loewner框架和系统识别方法。它甚至能够插值通过基于投影的方法构建的降阶模型和通过数据驱动方法构建的降阶模型。它的其他优点包括计算成本低，参数化降阶模型的尺寸小，对参数空间维的相对不敏感以及处理复杂参数依赖性的能力。它甚至能够插值通过基于投影的方法构建的降阶模型和通过数据驱动方法构建的降阶模型。它的其他优点包括计算成本低，参数化降阶模型的尺寸小，对参数空间维的相对不敏感以及处理复杂参数依赖性的能力。它甚至能够插值通过基于投影的方法构建的降阶模型和通过数据驱动方法构建的降阶模型。它的其他优点包括计算成本低，参数化降阶模型的尺寸小，对参数空间维的相对不敏感以及处理复杂参数依赖性的能力。