Rescaling time for task 1: ideal mass-spring

[SPronav]

Hi Sam,

I'm Srinivasa Pranav, a PhD student at CMU. We were interesting in recreating your experiments and comparing our method to HNNs.

In analyze-spring.ipynb, we had a hard time understanding why time is rescaled in the numerical integration using RK45 (from scipy's solve_ivp). This is in the integrate_models function under the "Quantitative Analysis" section:

# rescale time to compensate for noise effects, as described in appendix
t_span[1] *= 1 + .9*noise_std
t_eval *= 1 + .9*noise_std

This step has a significant impact on the results. We were unable to find information in the paper's appendix, so we hope you could guide us to a reference.
Also, since other experiments/tasks don't rescale time, we were interested to know why Task 1 requires it while other tasks do not.

Besides this, we really appreciate your efforts in neatly organizing your code and making it easy to understand.
Thank you!
Pranav