Abstract We introduce ML-FAIR, an automated implementation of the FAst Identification of mean-motion Resonances (FAIR) method in which unsupervised machine learning techniques are used to identify resonant patterns associated with two-body eccentricity-type mean-motion resonances. This method uses the geometric structure of resonant motion in an angle–angle phase space, where the resonance configuration is identified by counting the number of intersections of stripes with the horizontal and vertical axes. It automates the identification of resonance signatures using density-based clustering and circular kernel density estimation. By finding structured patterns in resonant angles, ML-FAIR classifies orbital behavior and identifies potential resonance ratios, thus reducing the need for extensive visual analysis. We used this approach to examine the Atira and Aten near-Earth asteroid populations and identify eccentricity-type resonant configurations with the terrestrial planets. ML-FAIR automatically screened more than 85% of the 2882 analyzed cases without manual inspection and provided candidate estimates of the associated resonance ratios, which were subsequently evaluated through resonant argument analysis. Comparison with results of a state-of-the-art long-timescale resonance identification method shows good qualitative consistency, with both methods identifying candidate populations in the same principal mean-motion resonances, except for a small number of cases, most notably the 3M:7 and 2M:5 resonances. The automated process significantly reduces the computational and manual effort required to analyze large-scale asteroid resonance surveys. These results demonstrate that ML-FAIR can efficiently detect mean-motion resonances in extensive asteroid catalogs and can facilitate future dynamical studies of resonant structures in complex dynamical regions.
Carruba et al. (2026) studied this question.