Li Meng, Bian Wenyu, Chen Liangxiong, Liu Mei
Zhangjiajie College, Zhangjiajie, China.
School of Public Administration, Hunan University, Changsha, China.
Front Neurorobot. 2024 Mar 12;18:1382305. doi: 10.3389/fnbot.2024.1382305. eCollection 2024.
This paper addresses the limitations of current neural ordinary differential equations (NODEs) in modeling and predicting complex dynamics by introducing a novel framework called higher-order-derivative-supervised (HiDeS) NODE. This method extends traditional NODE frameworks by incorporating higher-order derivatives and their interactions into the modeling process, thereby enabling the capture of intricate system behaviors. In addition, the HiDeS NODE employs both the state vector and its higher-order derivatives as supervised signals, which is different from conventional NODEs that utilize only the state vector as a supervised signal. This approach is designed to enhance the predicting capability of NODEs. Through extensive experiments in the complex fields of multi-robot systems and opinion dynamics, the HiDeS NODE demonstrates improved modeling and predicting capabilities over existing models. 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.
本文通过引入一种名为高阶导数监督（HiDeS）的神经常微分方程（NODE）的新框架，解决了当前神经常微分方程在建模和预测复杂动力学方面的局限性。该方法通过将高阶导数及其相互作用纳入建模过程，扩展了传统的NODE框架，从而能够捕捉复杂的系统行为。此外，HiDeS NODE使用状态向量及其高阶导数作为监督信号，这与传统的NODE不同，传统的NODE仅使用状态向量作为监督信号。这种方法旨在提高NODE的预测能力。通过在多机器人系统和舆论动态等复杂领域进行的大量实验，HiDeS NODE展示了比现有模型更好的建模和预测能力。这项研究不仅为动态系统提出了一个富有表现力和预测性的框架，还标志着NODE在多机器人系统和舆论动态领域的首次应用，暗示了未来跨学科工作的广阔潜力。代码可在https://github.com/MengLi-Thea/HiDeS-A-Higher-Order-Derivative-Supervised-Neural-Ordinary-Differential-Equation获取。
