Belief propagation for supply networks: Efficient clustering of their factor graphs
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We consider belief propagation (BP) as an efficient and scalable tool for state estimation and optimization problems in supply networks, in particular in power grids and natural gas pipeline networks. 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 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. The method outperforms existing alternatives to handle the loops. We point to other applications to supply networks such as water networks that share the structure of constraints in the form of analogues of 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 state determination, estimation, or optimization issues in supply networks.
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