We consider belief propagation (BP) as an efficient and scalable tool for
state estimation and optimization problems in supply networks such as power
grids. BP algorithms make use of factor graph representations, whose assignment
to the problem of interest is not unique. It depends on the state variables and
their mutual interdependencies. Many short loops in factor graphs may impede
the accuracy of BP. We propose a systematic way to cluster loops of naively
assigned factor graphs such that the resulting transformed factor graphs have
no additional loops as compared to the original network. They guarantee an
accurate performance of BP with only slightly increased computational effort,
as we demonstrate by a concrete and realistic implementation for power grids.
The method outperforms existing alternatives to handle the loops. We point to
other applications to supply networks such as gas-pipeline or other flow
networks that share the structure of constraints in the form of analogues to
Kirchhoff's laws. Whenever small and abundant loops in factor graphs are
systematically generated by constraints between variables in the original
network, our factor-graph assignment in BP complements other approaches. It
provides a fast and reliable algorithm to perform marginalization in tasks like
state determination, estimation, or optimization issues in supply networks.

本文提出了一种系统性的方式来对 naively 分配的因子图进行循环聚类，从而消除短路的影响，以提高 BP 算法在供应网络中的性能表现，实现了对供应网络中状态估计和优化问题的快速、可靠计算。