Speaker
Description
Simulating relativistic orbital dynamics around Schwarzschild black holes is essential for understanding general relativity and astrophysical phenomena like precession. Traditional numerical solvers face difficulty while dealing with noisy or sparse data, necessitating data-driven approaches. We develop a Scientific Machine Learning (SciML) framework to model orbital trajectories and symbolically recover the relativistic correction term. Neural Ordinary Differential Equations (Neural ODEs) accurately predict inverse radius $u$, radial velocity $v$, and precession $\delta$, performing well under ideal conditions. However, performance degrades with limited data or poor data quality.
To address this, we employ Universal Differential Equations (UDEs), which embed a neural network to approximate the correction term $\alpha \frac{GM}{c^2} u^3$, achieving precise orbit predictions even under challenging conditions. Symbolic regression further recovers an analytical expression closely matching the expected correction, with minimal error in fitted coefficients. We use adjoint-based training to quickly discover the best solution, and we achieve this in Julia with DiffEqFlux and Lux.
Using this method, we successfully demonstrate the ability to collect useful information for challenging assets by integrating machine learning with physical laws. This work can be further expanded for large-scale or detailed astrophysical projects.