Existing hypergraph network representation methods need to analyze the full batch nodes and hyperedges to recursively extend the neighbors across layers, which brings huge computational costs and leads to lower generalization accuracy due to over-expansion. To solve this problem, this study proposes a hypergraph network representation method based on importance sampling. First, the method treats nodes and hyperedges as two sets of independent identically distributed samples that satisfy specific probability measures and interprets the structural feature interactions of the hypergraph in an integral form. Second, it designs a neighbor importance sampling rule with learnable parameters and calculates sampling probabilities based on the physical relations and features of nodes and hyperedges. A fixed number of objects are recursively acquired layer by layer to construct a smaller sampled adjacency matrix. Finally, the spatial features of the entire hypergraph are approximated using Monte Carlo methods. In addition, with the advantage of physically informed neural networks, the sampling variance that needs to be reduced is added to the hypergraph neural network as a physical constraint to obtain sampling rules with better generalization capability. Extensive experiments on multiple datasets show that the method proposed in this study can obtain more accurate hypergraph representation results with a faster convergence rate.