A new framework for -optimal model reduction
A new framework for -optimal model reduction
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DOI：
10.1080/13873954.2018.1464030
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发表时间：
2017-09
影响因子：
1.9
通讯作者：
A. Castagnotto;B. Lohmann
中科院分区：
文献类型：
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作者：
A. Castagnotto;B. Lohmann
在这篇贡献中，提出了一个新的框架-最优约简，这是由（切向）插值和-最优近似的局部性质所驱动的。其主要优点是将缩减成本与优化成本解耦，从而大大加快了非最优缩减的速度。此外，一个中等大小的代理模型不需要额外的成本，可以用于误差估计等。数值实例说明了该框架在生成最优简化模型方面的有效性，且成本远低于传统算法。详细讨论了该框架在多输入多输出线性动力系统约简中的应用，并给出了最优性证明。本文最后简要讨论了如何将该框架扩展到其他系统类，从而表明这如何真正成为插值约简的一般框架。
ABSTRACT In this contribution, a new framework for -optimal reduction is presented, motivated by the local nature of both (tangential) interpolation and -optimal approximations. The main advantage is given by a decoupling of the cost of reduction from the cost of optimization, resulting in a significant speedup in -optimal reduction. In addition, a middle-sized surrogate model is produced at no additional cost and can be used e.g. for error estimation. Numerical examples illustrate the new framework, showing its effectiveness in producing -optimal reduced models at a far lower cost than conventional algorithms. Detailed discussions and optimality proofs are presented for applying this framework to the reduction of multiple-input, multiple-output linear dynamical systems. The paper ends with a brief discussion on how this framework could be extended to other system classes, thus indicating how this truly is a general framework for interpolatory reduction.