Stepwise reconstruction of higher-order networks from dynamics

Higher-order networks present great promise in network modeling, analysis, and control. However, reconstructing higher-order interactions remains an open problem. A significant challenge is the exponential growth in the number of potential interactions that need to be modeled as the maximum possible node number in an interaction increases, making the reconstruction exceedingly difficult. For higher-order networks, where higher-order interactions exhibit properties of lower-order dependency and weaker or fewer higher-order connections, we develop a reconstruction scheme integrating a stepwise strategy and an optimization technique to infer higher-order networks from time series. This approach significantly reduces the potential search space for higher-order interactions. Simulation experiments on a wide range of networks and dynamical systems demonstrate the effectiveness and robustness of our method.