Neural network analysis of S-star dynamics: implications for modified gravity

We studied the dynamics of S-stars in the Galactic center using the physics-informed neural networks. The neural networks are considered for both, Keplerian and the General Relativity dynamics, the orbital parameters for stars S1, S2, S9, S13, S31, and S54 are obtained, and the regression problem is solved. It is shown that the neural network is able to detect the Schwarzschild precession for S2 star, while the regressed part revealed an additional precession. Attributing the latter to a possible contribution of a modified gravity, we obtain a constraint for the weak-field modified General Relativity involving the cosmological constant which also deals with the Hubble tension. Our analysis shows the efficiency of neural networks in revealing the S-star dynamics and the prospects upon the increase in the amount and the accuracy of the observational data.