A Universal Physics-Informed Neural Network Framework for Predicting Network Dynamics: From Lower-Order to Higher-Order

Accurately predicting the complex networks dynamics is a challenging task. Many studies have shown that data-driven frameworks offer promising solutions to this issue. However, existing approaches still face significant limitations, particularly when network structures evolve from lower-order to higher-order networks, or when the dynamical equation of the network is governed by multiple dynamical terms, such as local self-dynamics, lower-order and higher-order coupling dynamics. To this end, we propose a universal physics-informed neural network framework capable of predicting various types of dynamics on both lower- and higher-order networks. First, the framework captures and integrates more nonlinear features through the higher-order term expansion module. Second, we design a hybrid neural network module to differentially learn each dynamical term to comprehensively capture network dynamics. Finally, a physics-informed loss function construction module is introduced to integrate differential loss with prediction loss, improving the accuracy of network dynamical prediction. Experimental results indicate that our method outperforms the state-of-the-art approaches in predicting network dynamics on both lower- and higher-order networks. Ablation studies confirm the critical role of each module. In addition, our method also performs well on real-world dynamical processes, which shows that it remains robust to real complex scenarios.