Machine Learning Analysis of DART Ejecta Dynamics and Predictability Limits

Predicting the long-term fate of ejecta generated by a kinetic impact in a binary asteroid system, such as the DART mission in the Didymos-Dimorphos pair, represents a highly complex dynamical challenge. The intrinsic chaotic nature of the system makes the classical N-bodies numerical integration highly sensitive to initial conditions. This thesis proposes a Machine Learning based predictive framework, designed to determine the fate of the ejecta (escape, quasi-stable orbit, or impact on one of the two bodies), providing a surrogate model for the iterative simulations. This research is developed through an incremental exploration of the feature space. Initially, statistical approaches based exclusively on the kinematic conditions at the time of impact were tested and, although they have proven efficient in determining the energetic boundaries for escaping ejecta, these models appeared to be structurally in- sufficient to disentangle the chaotic phase space and discriminate between impacts and quasi-stable orbits. To capture the non-linear orbital dynamics, the analysis moved to a time-series forecasting model, using the tsfresh Python package to extract features from time windows anchored to the ejection epoch. This preliminary approach high- lighted some limits, such as temporal aliasing and the long-term progressive decay of the dynamical signal. To overcome those limitations, the methodology evolved to a high-resolution sliding window paradigm. The input space was optimized through a physics-aware feature en- gineering process, filtering thousands of metrics and creating a set of common descrip- tors often used in celestial mechanics (e.g., absolute energy, FFT spectral signatures, complexity invariance, and radial trends). Multiple classification architectures, includ- ing XGBoost, a Multi-Layer Perceptron, and a custom-designed Hierarchical Classifier, were trained and validated through Nested Cross-Validation. The results, physically in- terpreted through Explainable AI (SHAP) techniques, demonstrated that the analysis of a brief observational time window (1-2 weeks) is sufficient to extract reliable features that allow the models to achieve fair predictive performances (reaching a macro F1- Score above 0.7) without the need for complete trajectory integration. Although it does not reach absolute accuracy due to the system’s inherent chaos, it offers a novel and promising analytical tool for space exploration and planetary defence. In particular, the developed methods will be instrumental in analyzing the trajectories of any particles identified by the Hera spacecraft in the vicinity of the binary.