Physics-Informed Neural Networks for Modeling Galactic Gravitational Potentials

TL;DR

This paper presents a neural network framework that incorporates physical laws to accurately model galactic gravitational potentials, capturing complex features while ensuring physical consistency.

Contribution

It introduces a Bayesian physics-informed neural network that models static and dynamic galactic potentials, integrating physical constraints with data-driven learning.

Findings

Achieves sub-percent mean acceleration error (0.14%) in mock systems.

Improves dynamical consistency over analytic baseline models.

Effectively models both static and time-dependent potentials.

Abstract

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 predictive 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 ($0.14\%$ mean acceleration error) and improves dynamical consistency compared to analytic baselines. This method complements existing analytic methods, enabling physics-informed baseline potentials to be combined with neural residual fields to achieve both interpretable and accurate potential models.