Figure 6.

(A) A plot of our initialization trajectories (in black) vs. the expected continuum limit solution (in red). The end point of each black trajectory, denoted by an orange star, corresponds to a value of R(t) that is used as a starting point for the flow training data. The noise evident in the simulated trajectories is caused by both randomness in the frequencies (each trajectory is a different sample from the distribution), and randomness in the arrangement of the oscillators with respect to their frequencies (only for the R ≈ 0 starting condition). (B) The approximately uniform sampling of the initial R-values R(t) used for flow generation. Note that a uniform distribution is not required, however it is desirable to facilitate training. It is only necessary that the values cover the range of R-space in order to allow us to learn the ODE over the entire [0, 1] domain.