A priori selection of augmentation perturbation magnitude for accurate map discovery

Determine an a priori rule or procedure for selecting the augmentation velocity-perturbation magnitude used to seed SINDy-based local Poincaré map discovery in the circular restricted three-body problem so that the resulting map is accurate, without requiring post hoc tuning.

Background

The mapping discovery relies on an augmentation strategy that perturbs initial conditions of nearby unstable periodic orbits with small velocity impulses to generate local section data for SINDy. The authors demonstrate that mapping accuracy and coefficient variance depend sensitively on the perturbation magnitude, δv, showing orders-of-magnitude changes in eigenvalue errors as δv varies.

However, the appropriate δv is not known beforehand, and the authors explicitly identify this as a challenge. They suggest that active learning could adaptively select δv, but establishing an a priori selection method remains unresolved.