用贝叶斯数据融合提升哈密顿系统长期预测精度
Learning Hamiltonian Dynamics with Bayesian Data Assimilation
- 基于神经网络构建哈密顿系统代理模型，保持能量守恒
- 引入自回归误差项，提升长时间序列预测准确性
- 结合实时观测数据动态修正，适合高精度物理建模
本文提出一种基于神经网络的未知哈密顿动力系统时间序列预测方法。该方法利用广义坐标（位置）及其共轭动量构建代理模型，确保哈密顿量恒定。为提升长期预测精度，引入自回归哈密顿神经网络，将自回归预测误差融入训练目标。同时采用贝叶斯数据融合技术，实时利用在线测量数据优化预测结果。在弹簧-质量系统及受引力扰动的高偏心率轨道上的数值实验表明，该方法能实现高精度、鲁棒的长期预测，具备实际应用潜力。
原文摘要 · Abstract (English)
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.
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