Hamiltonian mechanics is one of the cornerstones of natural sciences. Recently there has been significant interest in learning Hamiltonian systems in a free-form way directly from trajectory data. Previous methods have tackled the problem of learning from many short, low-noise trajectories, but learning from a small number of long, noisy trajectories, whilst accounting for model uncertainty has not been addressed. In this work, we present a Gaussian process model for Hamiltonian systems with efficient decoupled parameterisation, and introduce an energy-conserving shooting method that allows robust inference from both short and long trajectories. We demonstrate the method's success in learning Hamiltonian systems in various data settings.

翻译：哈密顿力学是自然科学的重要基石之一。近年来，直接从轨迹数据中以无约束形式学习哈密顿系统的方法引起了广泛关注。现有方法主要解决了从大量短时、低噪声轨迹中学习的问题，但尚未能处理从少量长时、带噪声轨迹中学习并考虑模型不确定性的挑战。本文提出了一种针对哈密顿系统的高斯过程模型，采用高效的解耦参数化方法，并引入了一种能量守恒的射出法，使得模型能够稳健地从短时和长时轨迹中进行推断。我们通过多种数据场景下的实验，验证了该方法在学习哈密顿系统方面的有效性。