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.
翻译:在文章中,我们研究从描述机械系统的“未贴标签的”普通差分方程式开始恢复港口-Hamiltonian系统结构的可能性。我们建议的算法可以分两个阶段解决问题。首先,利用机器学习方法构建系统的连通结构,从而绘制一个互连次子系统图。然后,通过恢复每个子系统的汉密尔顿结构以及相应的港口来增强这个图。第二阶段主要依赖我们简单描述的对流和普瓦森几何测量结果。精确的解决方法可以用计算机代数法和符号计算法来构建。算法允许将港口-Hamiltonian形式主义扩大到普通的普通差分方程式,从而最终引入了正常的OD形式的新概念。