Second-Order Message Passing Reservoir Computing for Nonlinear Systems

Given the data-driven nature of artificial intelligence models which do not require prior domain knowledge and system equations, along with the growing accessibility of observable or simulated data, we recognize the considerable potential of applying these models to nonlinear tracking controls. This paper proposes a second-order message passing reservoir computing model, whose effectiveness is validated in the simulation and prediction of complex nonlinear systems. In this model, neighboring information is aggregated through message passing to simulate interactions among entities within the network, and it outperforms Graph Neural Networks (GNNs). Its parallel structure also facilitates scalability, enabling it to be applicable to large networks. Additionally, we acknowledge that most accumulated data in real-world scenarios pertain to the observed temporal dynamics of entities, while acquiring their network topology is often challenging. To address this, we introduce a machine learning approach for systematic network reconstruction, treating the unknown topology as an optimization parameter. By minimizing the Mean Squared Error (MSE) through gradient descent, which inherently relies on data-driven optimization, we achieve an accurate reconstruction of the network topology. Consequently, our model successfully captures the dynamics of complex nonlinear systems even without the pre-existence of the network topology.