HiDeS: a higher-order-derivative-supervised neural ordinary differential equation for multi-robot systems and opinion dynamics - Li, Meng; Bian, Wenyu; Chen, Liangxiong; Liu, Mei (Frontiers in Neurorobotics, 2024)
Addressing the limitations of current neural ordinary differential equations (NODEs) in modeling and predicting complex dynamics, this paper introduces a higher-order-derivative-supervised (HiDeS) NODE. This approach extends traditional NODE frameworks by incorporating higherorder derivatives and their interactions into the modeling process, thereby enabling the capture of intricate system behaviors. Unlike conventional NODEs that utilize only the state vector as a supervised signal, HiDeS NODE employs both the state vector and its higher-order derivatives, significantly enhancing predictive accuracy. We demonstrate the superiority of HiDeS NODE through extensive experiments in multi-robot systems and opinion dynamics, areas where existing models struggle due to the complexity of interactions and dynamics. Our results indicate that HiDeS NODE offers improved modeling and prediction capabilities, paving the way for new applications in dynamic systems. This research not only proposes an expressive and predictive framework for dynamic systems but also marks the first application of NODEs to the fields of multi-robot systems and opinion dynamics, suggesting broad potential for future interdisciplinary work. The code is available at https://github.com/MengLi-Thea/HiDeS-A-Higher-Order-Derivative-Supervised-Neural-Ordinary-Differential-Equation.