论文标题
使用随机动态模型对不可分割的哈密顿系统的贝叶斯鉴定
Bayesian Identification of Nonseparable Hamiltonian Systems Using Stochastic Dynamic Models
论文作者
论文摘要
本文提出了一种用于系统识别（ID）的概率贝叶斯公式，并使用随机动态模型对不可分割的哈密顿系统进行了估计。非分离的哈密顿系统是来自不同科学和工程应用的模型，例如天体物理学，机器人技术，涡流动力学，带电的粒子动力学和量子力学。数值实验表明，与最新方法相比，所提出的方法以更高的精度和预测性不确定性降低了动态系统。结果进一步表明，在可能存在稀疏和嘈杂的测量的情况下，准确的预测远远超出了训练时间间隔，这为提出的方法提供了鲁棒性和概括性。定量益处是预测准确性，相对误差少于10％的相对误差超过12倍，比基于基准问题的基于最小二乘的方法长12倍。
This paper proposes a probabilistic Bayesian formulation for system identification (ID) and estimation of nonseparable Hamiltonian systems using stochastic dynamic models. Nonseparable Hamiltonian systems arise in models from diverse science and engineering applications such as astrophysics, robotics, vortex dynamics, charged particle dynamics, and quantum mechanics. The numerical experiments demonstrate that the proposed method recovers dynamical systems with higher accuracy and reduced predictive uncertainty compared to state-of-the-art approaches. The results further show that accurate predictions far outside the training time interval in the presence of sparse and noisy measurements are possible, which lends robustness and generalizability to the proposed approach. A quantitative benefit is prediction accuracy with less than 10% relative error for more than 12 times longer than a comparable least-squares-based method on a benchmark problem.
