Constraining the Cosmological Constant from Stellar Orbits Around Sgr A* Using Physics-Informed Neural Networks

We present a novel analytical framework employing Physics-Informed Neural Networks (PINNs) to constrain the cosmological constant $Λ$ through the analysis of stellar orbits around the supermassive black hole (SMBH) Sgr A* at the Galactic center. Focusing on the well-observed S2 star, we use an inverse PINN (iPINN) architecture to infer orbital elements and estimate the total precession angle from astrometric data. By isolating the contribution from $Λ$, which is defined as the difference between the total precession and the Schwarzschild precession, we derive a stringent upper bound of $Λ\leq 5.67 \times 10^{-40}, \mathrm{m}^{-2}$, which is approximately two orders of magnitude tighter than previous estimates obtained using similar data-driven methods. Extension of our analysis to two additional long-period S-stars, S1 and S9, reveals that while the cosmological precession becomes relatively more prominent in such systems, limited orbital coverage introduces significant uncertainties in parameter estimation. Among the cases examined, the constraint derived from S2 remains the most robust. Our results highlight the potential of PINN-based approaches for extracting physical insights from sparse or noisy astronomical data. Future applications to next-generation observational data and further methodological improvements in machine learning are expected to refine the cosmological constraints and enable broader tests of gravitational theories.