Machine Learning Assisted Dynamical Classification of Trans-Neptunian Objects

TL;DR

The paper tackles the problem of efficiently classifying Trans-Neptunian Objects into dynamical classes in the LSST era by developing a supervised gradient-boosting classifier. It builds a large, diverse training set (including substantial synthetic data) and engineers 227 time-series features from short and long numerical integrations to capture resonant and non-resonant dynamics, avoiding explicit resonant-angle analysis. The approach achieves high fidelity to human classifications, with overall accuracy around $97$–$98\%$ and dynamically relevant classifications exceeding $99.7\%$, and provides probabilistic assessments over clone ensembles (e.g., a 91\% resonance probability for a given TNO). This work demonstrates the viability and practicality of automated, scalable dynamical classification for upcoming LSST-sized TNO catalogs, enabling robust model-data comparisons and informing studies of outer solar system evolution.

Abstract

Trans-Neptunian objects (TNOs) are small, icy bodies in the outer solar system. They are observed to have a complex orbital distribution that was shaped by the early dynamical history and migration of the giant planets. Comparisons between the different dynamical classes of modeled and observed TNOs can help constrain the history of the outer solar system. Because of the complex dynamics of TNOs, particularly those in and near mean motion resonances with Neptune, classification has traditionally been done by human inspection of plots of the time evolution of orbital parameters. This is very inefficient. The Vera Rubin Observatory's Legacy Survey of Space and Time (LSST) is expected to increase the number of known TNOs by a factor of $\sim$10, necessitating a much more automated process. In this chapter we present an improved supervised machine learning classifier for TNOs. Using a large and diverse training set as well as carefully chosen, dynamically motivated data features calculated from numerical integrations of TNO orbits, our classifier returns results that match those of a human classifier 98% of the time, and dynamically relevant classifications 99.7% of the time. This classifier is dramatically more efficient than human classification, and it will improve classification of both observed and modeled TNO data.

Figures (7)

• Figure 1: Current inventory of 3357 multi-opposition TNOs with orbits sufficiently well-constrained to classify using the Gladman:2008 scheme. The top panels show perihelion distance vs semimajor axis (the grayed out areas are unphysical) while the bottom panels show ecliptic inclination vs semimajor axis. The right panels show a zoomed-out view over a larger parameter space range; note the log-scale for semimajor axis. The left panels show a zoomed-in view of the closer-in TNO populations; various prominent mean motion resonances with Neptune are labeled. The data underlying this plot is published in Volk:2024, and a version of this plot with a smaller sample of TNOs was published in Gladman:2021.
• Figure 2: Evolution of semimajor axis (top panels) and resonant angles (bottom panels) of the best-fit orbits of TNO 2013 UG17 in Neptune's 7:4 resonances (left panels) and TNO 534161 in Neptune's 3:2 resonances (right panels). The resonance angles are $\phi_{7:4} = 7\lambda - 4\lambda_N - 3\varpi$ and $\phi_{3:2} = 3\lambda - 2\lambda_N - \varpi$. TNO 534161's evolution is an example of clean, relatively low-amplitude resonant libration that is easily characterized using simple bounds on $\phi$. TNO 2013 UG17's evolution is a very typical example of intermittent libration that is more difficult to characterize, but its resonant nature is very readily recognized by an experienced human inspecting the evolution of $a$.
• Figure 3: Evolution of two clones of TNO 2014 UJ299 in semimajor axis (top panels) and resonant angle $\phi$ (bottom panels). The left panels show a clone librating in a high-order mixed-$e$-$i$-type resonance with resonant angle $\phi = 21\lambda - 13\lambda_N - 4\varpi - 4\Omega$, whereas the right panels show a nearby non-resonant clone. In each panel the time-axis is discontinuous with the left portion showing the high-resolution output from 0-0.5 Myr and the right portion showing lower-resolution output from 0.5-10 Myr. While the high-resolution output does reveal some differences in the semimajor axis behavior between the two clones, they look nearly identical over 10 Myr timescales. Their inclinations and eccentricities also evolve nearly identically. So we are left to ponder about the dynamical significance of the libration of this very high-order resonant argument.
• Figure 4: Top panel: Position of three TNO orbits (colored) and Neptune (black) over 10 Myr in a frame rotating at Neptune's instantaneous azimuthal rate. Bottom three panels: Barycentric distance, $r_b$ vs longitude angle relative to Neptune, $\theta_N$, at every output over the 10 Myr integrations for the three TNOs in the top panel. Neptune would be centered at the point (0,30.06) in these plots. We divide the evolution of the particle in this plane into a 10 by 20 grid, with the 10 bins in $r_b$ bounding the particle's minimum and maximum barycentric distances; the grid in $\theta_N$ starts and ends with half a bin so that Neptune is centered in the wrapped bin. We then calculate data features based on this grid, including: the number of empty grid spaces overall as well as in the smallest distance range (near perihelion) and the largest distance range (near aphelion); the average and standard deviation in the number of points in all the grid spaces as well as in the perihelion and aphelion grid spaces.
• Figure 5: Semimajor axis time-series for a 3:1 resonant object (top panels) and a non-resonant classical object (bottom panels). In the left panels, the time-axis is discontinuous with the first portion showing the high-resolution output over 0-0.5 Myr and the remaining portion showing lower-resolution output over 0.5-10 Myr. The right panels show the histogram of $a$ values across the 10 Myr integration, highlighting the difference between resonant and non-resonant evolution. In the machine learning classifier, the two data features,$r_{a,min-max}$ and $r_{a,em}$ related to the semimajor axis (see Table \ref{['t:features']}), encapsulate the information in these histograms.