约束力学系统的哈密顿量学习
Learning Hamiltonians of constrained mechanical systems
摘要：
最近，人们对使用神经网络对物理系统进行建模和计算的兴趣越来越大。哈密顿系统是经典力学中一种简洁的形式，其中动力学完全由一个标量函数哈密尔顿函数决定。解的轨迹往往被限制在线性向量空间的子流形上演化。在这项工作中，我们提出了新的方法来精确近似的哈密顿函数的约束力学系统给定的样本数据信息的解决方案。我们专注于使用显式李群积分器和其他经典计划的学习策略中的约束条件的保存的重要性。
英文摘要：
Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian systems are an elegant and compact formalism in classical mechanics, where the dynamics is fully determined by one scalar function, the Hamiltonian. The solution trajectories are often constrained to evolve on a submanifold of a linear vector space. In this work, we propose new approaches for the accurate approximation of the Hamiltonian function of constrained mechanical systems given sample data information of their solutions. We focus on the importance of the preservation of the constraints in the learning strategy by using both explicit Lie group integrators and other classical schemes.
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