一种无方程的粗粒度网络动力学方法
An equation-free approach to coarse-graining the dynamics of networks
摘要：
我们提出并说明了一种方法来粗粒化的动态不断变化的网络（网络的连接动态变化）。该方法基于无方程框架：详细网络演化模拟的短脉冲串与提升和限制算子相结合，这些算子在实际网络实现与其（适当选择的）粗观测值之间进行转换。这个框架在这里用于加速时间模拟（通过粗投影积分），并实现粗粒度的定点算法（通过无矩阵的牛顿-克雷洛夫GMRES）。该方法通过一个简单的网络演化的例子来说明，其中的粗粒度动力学的解析近似可以独立地获得，以验证计算结果。的范围和适用性的方法，以及良好的粗观测值的选择问题进行了讨论。
英文摘要：
We propose and illustrate an approach to coarse-graining the dynamics of evolving networks (networks whose connectivity changes dynamically). The approach is based on the equation-free framework: short bursts of detailed network evolution simulations are coupled with lifting and restriction operators that translate between actual network realizations and their (appropriately chosen) coarse observables. This framework is used here to accelerate temporal simulations (through coarse projective integration), and to implement coarsegrained fixed point algorithms (through matrix-free Newton-Krylov GMRES). The approach is illustrated through a simple network evolution example, for which analytical approximations to the coarse-grained dynamics can be independently obtained, so as to validate the computational results. The scope and applicability of the approach, as well as the issue of selection of good coarse observables are discussed.
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