A New Neural ODE Structure for Learning High-Order Dynamical Systems

Dynamical systems are mathematical descriptions of applications around our world. However, there are many challenges in control of dynamical systems, such as nonlinearity, uncertainty and high dimensionality. Recent research has revealed significant connections between neural networks and dynamical systems. Neural networks are powerful technologies that used for learning and predicting dynamical systems. Correspondingly, dynamical insights could be applied to neural networks. In this paper, we investigated neural network structures to learn highorder dynamical systems. We proposed a continuous high-order neural network structure based on Neural Ordinary Differential Equations to model high-order planar dynamical systems.