Title: Compact Recursive Models for Addressing the J2-Perturbed Lambert Problem

Abstract:

This study introduces TRM-PL (TRM-Perturbed Lambert), a rapid, recursive neural solver designed for the J2-perturbed Lambert problem. Built upon Tiny Recursive Models (TRM), this architecture derives its effective capacity from iteration depth rather than sheer parameter volume. The model operates within a two-level latent hierarchy, employing a weight-shared, compact reasoning module that is repeatedly applied. This process refines a candidate departure velocity by simulating the J2 trajectory and adjusting the result based on tracking errors. By combining initial-guess generation and iterative correction into one end-to-end differentiable framework, TRM-PL offers a learned alternative to the homotopy and continuation methods typical of classical perturbed-Lambert solvers. Instead of adhering to a hand-designed path from the Keplerian to the perturbed solution, the network autonomously learns its sequence of corrections.

We assessed the performance of TRM-PL across three test cases of escalating complexity: single-revolution low-Earth-orbit (LEO) transfers, multi-revolution LEO transfers, and multi-revolution Jovian transfers. The evaluation compared three distinct training paradigms: joint learning of the Lambert solution and J2 correction, refinement of the Lambert initial velocity using both target-position and J2-corrected velocity supervision, and refinement using target-position supervision exclusively. The results indicate that approaches relying solely on refinement are the most robust. Notably, the variant supervised only by target position significantly improved accuracy, reducing the median terminal-position error from 21.7 km to 0.027 km for single-revolution LEO transfers, and from 340.9 km to 0.31 km for multi-revolution LEO transfers, all while maintaining the same 2.3M-parameter architecture. Furthermore, applying a single Newton corrector iteration to the TRM-PL output reduced the median error for Jovian transfers to 0.063 km. These findings demonstrate that these compact models achieve the precision necessary for embedded deployment.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC