Diffusion Prediction and Control of Negative Information on Simplicial Complexes Using Physics-Informed Neural Networks

The inadequacy of traditional binary interaction networks in characterizing information flow processes within higher-order structures has driven growing research focus toward higher-order networks. Considering reporting mechanism and the dynamics of network scale, this paper proposes a susceptible-infected-quarantine-removed-empty (SIQRE) negative information diffusion model on simplicial complexes. An optimal control strategy, taking into account the system gain, is then implemented. The existence and stability of equilibria, and bi-stability between invasion threshold and persistence threshold are derived. Experiments on synthetic and empirical simplicial complexes reveal the dynamic behavior of the system with discontinuous phase transitions, backward bifurcation and periodic oscillations. An increase in the birth rate makes the system more susceptible to outbreaks of negative information, while the opposite is true for the death rate. Reporting mechanism suppresses discontinuous phase transition. And the synergistic application of preventive and corrective strategies demonstrates superior cost-effectiveness in system control compared to their isolated implementation. Additionally, an identifiability analysis of the model is conducted. Finally, the model parameters are inversely estimated and the diffusion dynamics are predicted using physics-informed neural networks (PINNs) across three instances, and the optimal control is subsequently performed, validating the effectiveness of both the proposed model and the control strategy.