Stateful ODE-Nets using Basis Function Expansions--Supplement Materials -- A Proofs A.1 Proof of Theorem

For more details, see [18, Chapter II.3]. The remainder of the proof follows by straightforward calculation. In one perspective, this changes the structure of the recurrent unit. ODE-Nets of [34] used general polynomial terms as one basis choice. Further, we use degree 7 quadrature rules.