arXiv：cs.LG· Sukru Caglar, Sena Kalabalik, Abdullah Umut Hamzaogullari, Arkadas Ozakin·· 11 小时前
用拉格朗日神经网络学习 Schwarzschild 测地线运动
Learning Schwarzschild Geodesic Motion with Lagrangian Neural Networks
AI 导读
研究者首次成功用拉格朗日神经网络（LNNs）训练 Schwarzschild 测地线动力学，通过解耦的位置—速度归一化方案和基于 ISCO 结构的能量约束对数均匀采样数据生成策略两项改进实现。模型能准确复现近日点进动与相对论时间膨胀，在绕中心质量多圈后能量与角动量守恒误差仍在百分之几以内，并在近距离、中距离和远场三类共八种轨道场景中预测轨迹。
正文
Abstract:Lagrangian Neural Networks (LNNs) learn dynamics from trajectory data by parameterizing a scalar Lagrangian and deriving accelerations through the Euler--Lagrange equation, providing a variational inductive bias that improves physical consistency over purely data-driven models. LNNs have recently been extended to general relativistic settings, leaving Schwarzschild geodesics as an open challenge. Training on complex relativistic systems is hindered by the diversity of the dynamics, as well as numerical instabilities and the difficulty of adequately sampling physically relevant, diverse orbital regimes. We introduce two coordinated improvements: a decoupled position--velocity normalization scheme that independently rescales each coordinate and its time derivatives, reweighting acceleration targets to balance contributions across all channels; and an energy-constrained log-uniformly sampled dataset generation strategy informed by the innermost stable circular orbit (ISCO) structure. With these improvements, our model accurately reproduces perihelion precession and relativistic time dilation, conserves energy and angular momentum to within a few percent even after completing multiple orbits around the central mass and predicts orbital trajectories across eight orbital scenarios in close, medium, and far-field regimes. These results establish that LNNs, augmented with physically motivated normalization and sampling, can reliably learn geodesic dynamics in curved spacetime. Our work also represents the first successful training of LNNs on Schwarzschild geodesics and offers a promising direction for data-driven modeling of complex relativistic systems.
| Subjects: | Machine Learning (cs.LG); General Relativity and Quantum Cosmology (gr-qc) |
| Cite as: | arXiv:2610.13234 [cs.LG] |
| (or arXiv:2610.13234v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2610.13234 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Arkadas Ozakin [view email]
[v1]
Fri, 9 Oct 2026 08:52:25 UTC (1,580 KB)
来源：arXiv：cs.LG · arxiv.org