复杂双曲网络的模型降阶
Model Reduction for Complex Hyperbolic Networks
摘要：
我们最近介绍了联合状态和参数约简的联合Gramian [C. Himpe和M.奥伯格大规模控制系统基于交叉格兰姆的状态和参数联合降阶。arXiv：1302.0634，2013]，其在这项工作中被应用以减少对双曲网络建模的参数化线性时变控制系统。该减少包括节点的维度和底层控制系统的参数。具有双曲结构的网络作为大系统的模型有许多应用。一个突出的例子是大脑，它的各个区域的网络结构通常被假设为信息传播的模型。具有许多节点的网络，以及参数化的，不确定的甚至未知的连接需要许多单独的计算成本高的模拟。所提出的模型降阶，使大量的模拟代理网络表现出几乎相同的动态与一个小的误差相比，全阶模型。
英文摘要：
We recently introduced the joint gramian for combined state and parameter reduction [C. Himpe and M. Ohlberger. Cross-Gramian Based Combined State and Parameter Reduction for Large-Scale Control Systems. arXiv:1302.0634, 2013], which is applied in this work to reduce a parametrized linear time-varying control system modeling a hyperbolic network. The reduction encompasses the dimension of nodes and parameters of the underlying control system. Networks with a hyperbolic structure have many applications as models for large-scale systems. A prominent example is the brain, for which a network structure of the various regions is often assumed to model propagation of information. Networks with many nodes, and parametrized, uncertain or even unknown connectivity require many and individually computationally costly simulations. The presented model order reduction enables vast simulations of surrogate networks exhibiting almost the same dynamics with a small error compared to full order model.
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