  Hypergraph networks are closer to real life because they can reflect
higher-order interactions, so researchers have begun using them to build models
for real-world networks. The mean-field approach is the current tool for
studying the percolation problem on hypergraph networks. However, we found that
when there is a loop in the hypergraph network, the calculated results using
this approach deviate from the real results. Therefore, in this paper, we
rephrase the percolation on the hypergraph network as a message passing
process, thus obtaining a message passing approach. Our proposed approach has
been tested in several hypergraph networks with loops, and the experimental
results are more accurate than those under the mean-field approach. This is
helpful to analyze and understand the robustness of hypergraph networks with
loops. In addition, we also specifically analyzed how four different types of
loops affect the accuracy of the experiment. Our proposed message passing
approach also provides another way to study percolation on hypergraph networks.
