SIPHy：从含噪数据中稀疏识别端口-哈密顿系统
SIPHy: Sparse identification of port-Hamiltonian systems from noisy data
AI总结：
提出SIPHy方法，结合哈密顿流样条，从含噪轨迹数据中稀疏识别端口-哈密顿系统，联合估计哈密顿函数、耗散和输入矩阵，提升模型可解释性与泛化能力。
AI中文摘要：
我们提出了端口-哈密顿系统的稀疏识别方法（SIPHy），该方法能够从含噪的轨迹观测数据中进行保结构的符号回归。该方法适用于端口-哈密顿系统，这类系统为描述涉及能量交换、耗散和控制的动力系统提供了一个通用框架。我们的算法能够联合识别哈密顿函数以及耗散矩阵和输入矩阵。此外，我们引入了哈密顿流样条，以更好地逼近受噪声污染或存在缺失时间点的轨迹数据的导数，这是微分方程系统识别中的一个主要挑战。该方法将分段多项式哈密顿量的流进行组装，以产生用于稀疏回归的光滑、可微的轨迹。将流样条与SIPHy相结合，可以从含噪和不完整的轨迹数据中生成可解释的、基于物理的模型。由于哈密顿函数、耗散矩阵和输入矩阵被识别为独立的组件，所得模型可以在训练期间从未观察到的控制输入和耗散机制下进行模拟，从而提高了模型发现方法的鲁棒性和泛化能力。
英文摘要：
We propose sparse identification of port-Hamiltonian systems (SIPHy), enabling structure-preserving symbolic regression from noisy trajectory observations. The method applies to port-Hamiltonian systems, which provide a general framework for describing dynamical systems in terms of energy exchange, dissipation and control. Our algorithm can jointly identify the Hamiltonian as well as the dissipation and input matrices. Furthermore, we introduce Hamiltonian flow splines to better approximate derivatives of trajectory data corrupted by noise or with missing time points, a major challenge of system identification for differential equations. This method assembles flows of piecewise polynomial Hamiltonians to produce a smooth, differentiable trajectory necessary for sparse regression. Combining flow splines with SIPHy yields interpretable, physically grounded models from noisy and incomplete trajectory data. Because the Hamiltonian, dissipation, and input matrices are identified as separate components, the resulting models can be simulated under control inputs and dissipation regimes never observed during training, thus improving the robustness and generalization capabilities of model discovery methods.
