  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 of the amount and the accuracy of
the observational data.
