| There are a variety of complex systems in the real world,such as ecosystems,social networks,etc.The dynamics on these complex networks are usually modelled using differential equations to represent various complex phenomena.However,the underlying dynamics of a significant number of complex systems are currently unknown.Therefore,developing a data-driven learning method to understand the underlying principles of complex network dynamics is the first step towards implementing interventions and controls on them,and is of considerable practical importance in challenges such as climate disaster prediction and interrupting the spread of infectious diseases.With the popularity of deep learning research,deep learning methods related to processing graph data have been fully developed,and graph neural networks have become a current research hotspot with their excellent performance.Modelling the dynamics on complex networks based on graph neural networks opens up a new research direction for current complex systems research.Based on the above issues,the main work of this paper is as follows:(1)This paper finds that current research related to modelling the dynamics of complex networks exposes an under-recognised misconception that the idea of embedding node features into potential spaces in graph neural networks is naturally adopted by many neural dynamic models on complex networks.However,while the high-dimensional embedding allows the model to fit the observed data well,it does not properly learn the dynamics that express the observed data.Previous research has been limited to short-term prediction tasks of dynamical dynamics,where fitting in high-dimensional space provides good predictions,but rapidly breaks down in long-term prediction tasks.To address these issues,this paper proposes three test criteria that dynamical prediction tasks should satisfy,demonstrates through empirical analysis of the results that embedding-based models fail the three test criteria,and analyses the reasons for the failure of embedded models,particularly in a topological conjugate perspective for theoretical analysis.(2)By demonstrating that unreasonable embeddings lead to these challenges,this paper proposes a simple embedding-free modelling approach based on parameterising two vector field components,namely the complex network neural dynamics model(Dy-Net Neural Dynamics).It is experimentally verified that the model in this paper is able to reliably learn a class of dynamical phenomena on different topologies.As it models observations directly in physical space,the learning parameters of the model are topology-independent and naturally have topological migration capabilities.The models capture autodynamics and interaction dynamics separately,and the model parameters trained in each of the two vector fields can be transformed into intuitive mathematical expressions by introducing symbolic regression,enhancing the interpretability of the models.This provides significant performance advantages and reliability over previously proposed data-driven neurodynamic models for complex networks. |
