Predicting Higher-order Dynamics without Network Topology by Ridge Regression

The prediction of future dynamics on networks is a challenge. Unfortunately, due to the noise in the sampling process, or the low resolution of observational data, it is hardly feasible to get the complete topology of real-world networks. Moreover, the higher-order interactions among nodes add the difficulty to accurate prediction of dynamics on networks. In this work, we proposed a two-step approach for higher-order dynamics prediction without network topology. First, the observations of nodal dynamics of a specific dynamical model on unknown hypergraphs are collected to solve an optimization problem by Ridge regression, to obtain a surrogate incidence matrix. Second, the prediction is obtained by iterating the equation of the dynamical model with the surrogate incidence matrix. We define the average relative prediction error to evaluate the performance of our prediction method, and a wide range of hypergraph dynamics with different parameters are predicted. The prediction accuracy is positively correlated with the number of hyperedges the hypergraph contains and the contact rate in the dynamical model.