论文标题
与神经网络的哈密顿系统的学习轨迹
Learning Trajectories of Hamiltonian Systems with Neural Networks
论文作者
论文摘要
使用神经网络对保守系统进行建模是一个积极研究的领域。一种流行的方法是使用哈密顿神经网络（HNNS），该神经网络依赖于以汉密尔顿运动方程式描述保守系统的假设。许多最近的作品着重于改善培训HNN时使用的集成方案。在这项工作中，我们建议使用附加的神经网络对建模系统的连续时间轨迹进行估算，以增强HNN，这在文献中称为“深度隐藏的物理模型”。我们证明了所提出的集成方案非常适合HNN，尤其是采样率，嘈杂和不规则观察结果。
Modeling of conservative systems with neural networks is an area of active research. A popular approach is to use Hamiltonian neural networks (HNNs) which rely on the assumptions that a conservative system is described with Hamilton's equations of motion. Many recent works focus on improving the integration schemes used when training HNNs. In this work, we propose to enhance HNNs with an estimation of a continuous-time trajectory of the modeled system using an additional neural network, called a deep hidden physics model in the literature. We demonstrate that the proposed integration scheme works well for HNNs, especially with low sampling rates, noisy and irregular observations.
