Learning Schwarzschild Geodesic Motion with Lagrangian Neural Networks

The paper presents a method for training Lagrangian Neural Networks (LNNs) to learn Schwarzschild geodesic motion. By introducing a decoupled position–velocity normalization and an energy-constrained log-uniform sampling strategy, the authors achieve accurate reproduction of perihelion precession, relativistic time dilation, and conservation of energy and angular momentum across diverse orbital regimes. This work marks the first successful training of LNNs on Schwarzschild geodesics and demonstrates their potential for data-driven modeling of complex relativistic systems.

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