具有输出误差噪声模型的端口-Hamiltonian神经网络
Port-Hamiltonian Neural Networks with Output Error Noise Models
AI总结：
针对HNN难以处理外部输入、耗散和含噪测量的问题，提出融合端口-Hamiltonian理论、OE噪声模型与SUBNET辨识的OE-pHNN框架，实现复杂动态系统的一致、可靠建模。
摘要：
Hamiltonian神经网络（HNN）代表了一类很有前景的物理信息深度学习方法，它将Hamiltonian理论作为神经网络中的基础知识。然而，其直接应用于工程系统时，常受到外部输入、耗散和含噪测量等实际问题的挑战。本文提出了一个新颖框架，用于增强HNN处理这些现实因素的能力。我们将端口-Hamiltonian理论集成到神经网络结构中，使其能够包含外部输入和耗散，同时通过输出误差（OE）模型结构减轻测量噪声的影响。由此得到的输出误差端口-Hamiltonian神经网络（OE-pHNN）可适配于处理含噪测量下复杂工程系统的建模问题。此外，我们提出基于子空间编码器方法（SUBNET）辨识OE-pHNN，该方法利用数据子段高效近似完整仿真损失，并使用编码器函数预测初始状态。通过将SUBNET与OE-pHNN结合，我们在含噪测量条件下获得了复杂工程系统的一致性模型。此外，我们进行了一致性分析，以确保所提出的数据驱动模型学习方法的可靠性。我们在系统辨识基准上证明了该方法的有效性，显示其作为现实应用中动态系统建模强大工具的潜力。
英文摘要：
Hamiltonian neural networks (HNNs) represent a promising class of physics-informed deep learning methods that utilize Hamiltonian theory as foundational knowledge within neural networks. However, their direct application to engineering systems is often challenged by practical issues, including the presence of external inputs, dissipation, and noisy measurements. This paper introduces a novel framework that enhances the capabilities of HNNs to address these real-life factors. We integrate port-Hamiltonian theory into the neural network structure, allowing for the inclusion of external inputs and dissipation, while mitigating the impact of measurement noise through an output-error (OE) model structure. The resulting output error port-Hamiltonian neural networks (OE-pHNNs) can be adapted to tackle modeling complex engineering systems with noisy measurements. Furthermore, we propose the identification of OE-pHNNs based on the subspace encoder approach (SUBNET), which efficiently approximates the complete simulation loss using subsections of the data and uses an encoder function to predict initial states. By integrating SUBNET with OE-pHNNs, we achieve consistent models of complex engineering systems under noisy measurements. In addition, we perform a consistency analysis to ensure the reliability of the proposed data-driven model learning method. We demonstrate the effectiveness of our approach on system identification benchmarks, showing its potential as a powerful tool for modeling dynamic systems in real-world applications.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
