Abstract
In this paper, we develop a neural network-based approach for time-series prediction in unknown Hamiltonian dynamical systems. Our approach leverages a surrogate model and learns the system dynamics using generalized coordinates (positions) and their conjugate momenta while preserving a constant Hamiltonian. To further enhance long-term prediction accuracy, we introduce an Autoregressive Hamiltonian Neural Network, which incorporates autoregressive prediction errors into the training objective. Additionally, we employ Bayesian data assimilation to refine predictions in real-time using online measurement data. Numerical experiments on a spring-mass system and highly elliptic orbits under gravitational perturbations demonstrate the effectiveness of the proposed method, highlighting its potential for accurate and robust long-term predictions.
Abstract (translated)
在这篇论文中，我们开发了一种基于神经网络的方法，用于未知哈密顿动力系统的时序预测。我们的方法利用了替代模型，并通过广义坐标（位置）及其共轭动量来学习系统动态，同时保持恒定的哈密顿函数不变。为了进一步提高长期预测的准确性，我们引入了一种自回归哈密顿神经网络，该网络将自回归预测误差纳入训练目标中。此外，我们还采用了贝叶斯数据同化方法，在线利用测量数据实时改进预测。在弹簧-质量系统和受引力摄动影响的高度椭圆轨道上的数值实验展示了所提出方法的有效性，并突显了其进行准确且稳健的长期预测的巨大潜力。
URL
https://arxiv.org/abs/2501.18808
