论文标题
学习 - 哈米尔顿港系统 - 算法
Learning port-Hamiltonian systems -- algorithms
论文作者
论文摘要
在本文中，我们研究了从描述机械系统的``未标记''普通微分方程开始恢复港口港口系统结构的可能性。我们建议该算法分为两个阶段解决问题。它首先使用机器学习方法构建系统的连接结构 - 因此产生了相互联系的子系统的图。然后，通过恢复每个子系统的哈密顿结构以及相应的端口来增强该图。第二阶段在很大程度上取决于我们简要绘制的符号和泊松几何形状的结果。可以使用计算机代数和符号计算方法来构建精确的解决方案。该算法允许将哈米顿港形式主义扩展到通用的普通微分方程，因此最终引入了正常形式的ODES的新概念。
In this article we study the possibilities of recovering the structure of port-Hamiltonian systems starting from ``unlabelled'' ordinary differential equations describing mechanical systems. The algorithm we suggest solves the problem in two phases. It starts by constructing the connectivity structure of the system using machine learning methods -- producing thus a graph of interconnected subsystems. Then this graph is enhanced by recovering the Hamiltonian structure of each subsystem as well as the corresponding ports. This second phase relies heavily on results from symplectic and Poisson geometry that we briefly sketch. And the precise solutions can be constructed using methods of computer algebra and symbolic computations. The algorithm permits to extend the port-Hamiltonian formalism to generic ordinary differential equations, hence introducing eventually a new concept of normal forms of ODEs.
