Physics-Informed Neural Networks for Modeling Galactic Gravitational Potentials

We introduce a physics-informed neural framework for modeling static and time-dependent galactic gravitational potentials. The method combines data-driven learning with embedded physical constraints to capture complex, small-scale features while preserving global physical consistency. We quantify uncertainty through a Bayesian framework, and model time evolution using a neural ODE approach. Applied to mock systems of varying complexity, the model achieves reconstruction errors at the sub-percent level and improves dynamical consistency compared to analytic baselines.