Comparative analysis of Neural Networks approaches for Initial Orbit Determination of Near-Earth Objects

Initial Orbit Determination (IOD) from Very Short Arcs (VSAs) remains one of the most challenging open problems in asteroid surveillance and celestial mechanics. Classical methods require angular observations spanning a sufficient fraction of the orbit, and become ill-conditioned or fail outright when only a single observing night is available, as is the case for most newly discovered Near-Earth Objects (NEOs). We present a comparative analysis of two Neural Network (NN) models that attack the ranging problem directly: both ingest a triplet of time-tagged angular measurements (t i,α i,δ i), i=1,2,3, from a single VSA and predict the geocentric range and range-rate (ρ, ρ), thus completing the orbital state vector. The first is a Multi-Layer Perceptron trained on a purely data-driven objective; the second augments it with a physics-informed loss. Both are trained, under an object-disjoint partition, on a sample of the 568,127 VSAs of 39,031 real NEOs available in the NEODyS-2 catalogue. Each model returns an estimate on every arc by construction, so we assess instead whether that estimate is dynamically admissible: on a held-out test set of 56,773 arcs the physics-informed model places 85.1% of its predictions inside the admissible region, against 76.5% for the data-driven baseline, whereas Gauss's and Laplace's methods return a solution on only 45.0% and 47.3% of the same arcs and collapse onto the degenerate root in about nine of those cases out of ten. A stratified analysis over proper motion and true range shows that the physics-informed objective is not uniformly superior to the baseline: it trades a longer error tail for admissibility and for a marked advantage on the fast, nearby arcs that are operationally the most relevant.