Machine learning prediction for mean motion resonance behaviour -- The planar case

TL;DR

This paper demonstrates that a trained neural network can accurately predict the long-term behavior of objects in 2:3 mean motion resonance with Neptune, offering a fast alternative to traditional numerical simulations for classifying Kuiper Belt objects.

Contribution

The study introduces a neural network model capable of predicting the dynamics of 2:3 resonance objects over extended periods, improving efficiency in resonance classification.

Findings

Neural network predicts resonant angles with a few degrees accuracy.

ANN can effectively measure resonant amplitudes.

Method significantly reduces computational time for resonance analysis.

Abstract

Most recently, machine learning has been used to study the dynamics of integrable Hamiltonian systems and the chaotic 3-body problem. In this work, we consider an intermediate case of regular motion in a non-integrable system: the behaviour of objects in the 2:3 mean motion resonance with Neptune. We show that, given initial data from a short 6250 yr numerical integration, the best-trained artificial neural network (ANN) can predict the trajectories of the 2:3 resonators over the subsequent 18750 yr evolution, covering a full libration cycle over the combined time period. By comparing our ANN's prediction of the resonant angle to the outcome of numerical integrations, the former can predict the resonant angle with an accuracy as small as of a few degrees only, while it has the advantage of considerably saving computational time. More specifically, the trained ANN can effectively measure the resonant amplitudes of the 2:3 resonators, and thus provides a fast approach that can identify the resonant candidates. This may be helpful in classifying a huge population of KBOs to be discovered in future surveys.