Table 2.

Main symbols and notations.

Symbol	Description
x	State vector representing opinions of individuals
t	Time variable
$\stackrel{.}{x}$	First-order time derivatives of x
$\ddot{x}$	Second-order time derivatives of x
$\stackrel{\mathrm{...}}{x}$	Third-order time derivatives of x
c	Order of the highest derivative in HiDeS NODE
x (c)	c-th order time derivative of x
θ	Parameters of a neural network
ϕθ(·)	Vector field (neural network) parameterized by θ
ℝd	d-dimensional real space
ℝn	n-dimensional real space
ω	Extended state vector in HiDeS NODE
Δt	Time step for numerical approximation
ϑ	Alternate set of parameters for the neural network
$\stackrel{\vee }{t},\widehat{t}$	Time interval boundaries