用哈密顿神经网络模拟毛球模型中的粒子轨迹，精度媲美传统方法。
Hamiltonian Neural Networks approach to fuzzball geodesics
- 构建哈密顿神经网络求解毛球几何下的运动方程
- 在不同碰撞参数下实现高精度轨迹预测，包括不稳定轨道
- 相比传统数值积分器更稳定，适合复杂物理场景
计算资源和数据的增加推动了机器学习在物理数据分析中的应用。然而，将机器学习用于求解复杂物理系统微分方程的工作在理论高能物理中仍不普遍。哈密顿神经网络（HNNs）通过最小化损失函数来求解哈密顿运动方程。本文实现了多个HNN模型，训练后能高精度求解质量为零的探测粒子在平滑无视界几何——D1-D5圆环毛球内的哈密顿方程。研究涵盖了平面（赤道）与非平面测地线，在不同碰撞参数下的多种情形，部分轨迹存在不稳定性。结果表明，HNNs可望替代标准数值积分器，其精度相当但临界情况下更可靠。
原文摘要 · Abstract (English)
The recent increase in computational resources and data availability has led to a significant rise in the use of Machine Learning (ML) techniques for data analysis in physics. However, the application of ML methods to solve differential equations capable of describing even complex physical systems is not yet fully widespread in theoretical high-energy physics. Hamiltonian Neural Networks (HNNs) are tools that minimize a loss function defined to solve Hamilton equations of motion. In this work, we implement several HNNs trained to solve, with high accuracy, the Hamilton equations for a massless probe moving inside a smooth and horizonless geometry known as D1-D5 circular fuzzball. We study both planar (equatorial) and non-planar geodesics in different regimes according to the impact parameter, some of which are unstable. Our findings suggest that HNNs could eventually replace standard numerical integrators, as they are equally accurate but more reliable in critical situations.
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