供应网络的置信传播：因子图的有效聚类
Belief propagation for supply networks: Efficient clustering of their factor graphs
摘要：
我们认为置信传播（BP）作为一个有效的和可扩展的工具，状态估计和优化问题的供应网络，如电网。BP算法利用因子图表示，其分配给感兴趣的问题是不唯一的。它取决于状态变量及其相互依赖性。因子图中的许多短循环可能会影响BP的准确性。我们提出了一种系统的方法来聚类天真分配的因子图的循环，使得所得到的转换因子图与原始网络相比没有额外的循环。他们保证BP的准确性能，只有轻微增加的计算工作量，我们证明了一个具体的和现实的实现电网。该方法在处理循环方面优于现有的替代方法。我们指出，其他应用程序，如天然气管道或其他流量网络，共享的约束结构的形式类似于基尔霍夫定律的供应网络。每当因子图中的小而丰富的循环是由原始网络中变量之间的约束系统地生成时，我们在BP中的因子图分配补充了其他方法。它提供了一种快速可靠的算法，用于在供应网络中的状态确定，估计或优化问题等任务中执行边缘化。
英文摘要：
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.
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