In order to make data-driven models of physical systems interpretable and
reliable, it is essential to include prior physical knowledge in the modeling
framework. Hamiltonian Neural Networks (HNNs) implement Hamiltonian theory in
deep learning and form a comprehensive framework for modeling autonomous
energy-conservative systems. Despite being suitable to estimate a wide range of
physical system behavior from data, classical HNNs are restricted to systems
without inputs and require noiseless state measurements and information on the
derivative of the state to be available. To address these challenges, this
paper introduces an Output Error Hamiltonian Neural Network (OE-HNN) modeling
approach to address the modeling of physical systems with inputs and noisy
state measurements. Furthermore, it does not require the state derivatives to
be known. Instead, the OE-HNN utilizes an ODE-solver embedded in the training
process, which enables the OE-HNN to learn the dynamics from noisy state
measurements. In addition, extending HNNs based on the generalized Hamiltonian
theory enables to include external inputs into the framework which are
important for engineering applications. We demonstrate via simulation examples
that the proposed OE-HNNs results in superior modeling performance compared to
classical HNNs.

本文提出了一种基于输出误差 Hamiltonian Neural Network (OE-HNN) 建模方法，以解决带有输入和嘈杂状态测量的实物系统建模的问题，并扩展了 HNNs 的广义 Hamiltonian 理论，演示了此方法相对于传统的 HNNs 在建模性能方面的卓越优势。