论文标题
通过频率域有理替代物的插值来降低非侵入性双绿色参数模型
Non-intrusive double-greedy parametric model reduction by interpolation of frequency-domain rational surrogates
论文作者
论文摘要
我们为参数动力学系统的非侵入性替代建模提供了一种模型订购方法。整个参数空间上的还原模型是通过仅在频率中组合的，该替代物在参数的几个选定值中构建。特别是，这需要通过解决优化问题来匹配各自的极点。如果频率替代物是通过适当的合理插值策略构建的，则可以以自适应方式对频率和参数进行采样。通常，这会产生不同数量的杆子的频率替代，这是我们提出的算法解决的情况。此外，我们通过在参数空间中采用局部精制的稀疏网格来削弱维度的诅咒，即使在高维设置中也可以应用我们的方法。数值示例用于展示该方法的有效性，并突出显示其在处理不平衡杆匹配以及大量参数方面的一些局限性。
We propose a model order reduction approach for non-intrusive surrogate modeling of parametric dynamical systems. The reduced model over the whole parameter space is built by combining surrogates in frequency only, built at few selected values of the parameters. This, in particular, requires matching the respective poles by solving an optimization problem. If the frequency surrogates are constructed by a suitable rational interpolation strategy, frequency and parameters can both be sampled in an adaptive fashion. This, in general, yields frequency surrogates with different numbers of poles, a situation addressed by our proposed algorithm. Moreover, we explain how our method can be applied even in high-dimensional settings, by employing locally-refined sparse grids in parameter space to weaken the curse of dimensionality. Numerical examples are used to showcase the effectiveness of the method, and to highlight some of its limitations in dealing with unbalanced pole matching, as well as with a large number of parameters.
