Schematic of the relation between the operators f, g, φ, and ψ employed in the current setup. The ODE system , ℝ^N → ℝ^N, allows the integration of in time, and is analogous to , ℝ^M → ℝ^M that is employed to integrate . To transform to (and vice versa) we use an encoder φ, ℝ^N → ℝ^M, and a decoder ψ, ℝ^M → ℝ^N.To evolve both and we employ a standard implicit ODE solver, hence the time-step ∆t can be arbitrarily long.