We show the similarities between our method, Neural ODE, and differentiable physics in Figure 4. All the three approaches have a differentiable system governed by some kinds of differential equations. Our method parametrizes the dynamics using continuous basis functions; Neural ODE uses neural networks; and Differentiable physics describes the dynamics system using physics equations like Newton's Second Law, Navier-Stokes equations. Let Uv(t2,t1) be as defined in Theorem 3.2. Let Lbe defined as (4), and H(v,t) = P jfj(v,t)Hj.

Two types of expression of empirical interest have been studied: sentences in English and other'natural' languages, and programs written in some high-level procedural language like ALGOL. Expressions in these languages consist of sets of elements (words and characters) co-ordinated with one another according to the sensorily manifest relationship'alongside', more commonly termed'followed by'.

Grammars or syntax specifications address themselves to the characterisation in symbolic terms of the structure of complex expressions. Two types of expression of empirical interest have been studied: sentences in English and other'natural' languages, and programs written in some high-level procedural language like ALGOL. Expressions in these languages consist of sets of elements (words and characters) coordinated with one another according to the sensorily manifest relationship'alongside', more commonly termed'followed by'.