Single- vs. Multilayer Physics-Informed Extreme Learning Machines for Orbit Determination

Orbit Determination (OD) is commonly addressed with classical estimators such as Weighted Least Squares, which are statistically well founded but can be sensitive to poor initialization and may degrade when the initial state is weakly known. Physics-Informed Machine Learning offers an alternative by embedding orbital dynamics directly into the estimation process. In this work, Physics-Informed Extreme Learning Machines (PIELMs) are investigated as fast OD models that do not require a high-quality initial guess, since the output layer is obtained from a physics-based training objective that enforces consistency with both measurements and dynamics.

While single-layer PIELMs can achieve high accuracy, they may exhibit reduced stability in regimes with limited measurement support. To improve representational capacity and generalization, the Deep PIELM augments the model with an autoencoder-based feature hierarchy that is pretrained efficiently via the Moore–Penrose pseudoinverse, followed by physics-informed nonlinear least-squares optimization of the final layer.

Comparative results highlight the trade-offs among classical least squares, single-layer PIELM, and Deep PIELM in terms of OD accuracy, robustness under poor initialization, and computational efficiency under sparse optical and range measurements from a limited set of ground stations. For suitable hyperparameter configurations, the multilayer architecture provides improved stability and accuracy over the single-layer variant while retaining low training times, positioning Deep PIELMs as an effective complement to classical least-squares OD when robust performance without reliable initial guesses is required. The presented work is part of the Artificial Intelligence for Precise Orbit Determination project.