用输入输出数据学习物理一致的动力学模型，无需速度或动量测量。
Learning Dynamics from Input-Output Data with Hamiltonian Gaussian Processes
- 基于哈密顿高斯过程，从输入输出数据推断隐藏状态和系统参数。
- 在非保守系统中有效建模能量交换，如外部力和耗散。
- 全贝叶斯框架可同时估计不确定性、超参数和阻尼系数。
将能量守恒等非约束性先验知识融入学习方法，是利用有限数据构建物理一致动力学模型的关键，适用于模型预测控制等场景。近期研究将哈密顿动力学引入高斯过程（GPs），获得具备不确定性量化能力且能量守恒的模型，但这类方法依赖罕见的速率或动量数据。本文研究仅从输入输出数据学习动力学，不依赖速度或动量测量。采用非保守形式，可捕捉与环境的能量交换，如外力或耗散。提出全贝叶斯方案，联合估计未知隐藏状态、GP超参数及结构超参数（如阻尼系数）的概率密度。在非线性仿真案例中评估，并与依赖动量测量的先进方法对比。
原文摘要 · Abstract (English)
Embedding non-restrictive prior knowledge, such as energy conservation laws, into learning methods is a key motive to construct physically consistent dynamics models from limited data, relevant for, e.g., model-based control. Recent work incorporates Hamiltonian dynamics into Gaussian Processes (GPs) to obtain uncertainty-quantifying, energy-consistent models, but these methods rely on -- rarely available -- velocity or momentum data. In this paper, we study dynamics learning using Hamiltonian GPs and focus on learning solely from input-output data, without relying on velocity or momentum measurements. Adopting a non-conservative formulation, energy exchange with the environment, e.g., through external forces or dissipation, can be captured. We provide a fully Bayesian scheme for estimating probability densities of unknown hidden states, GP hyperparameters, as well as structural hyperparameters, such as damping coefficients. The proposed method is evaluated in a nonlinear simulation case study and compared to a state-of-the-art approach that relies on momentum measurements.
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