Hybrid machine learning based on Hamiltonian formulations has recently been successfully demonstrated for simple mechanical systems. In this work, we stress-test the method on both simple mass-spring systems and more complex and realistic systems with several internal and external ports, including a system with multiple connected tanks. We quantify performance under various conditions and show that imposing different assumptions greatly affects the performance, highlighting advantages and limitations of the method. We demonstrate that port-Hamiltonian neural networks can be extended to higher dimensions with state-dependent ports. We consider learning on systems with known and unknown external ports. The port-Hamiltonian formulation allows for detecting deviations and still provide a valid model when the deviations are removed. Finally, we propose a symmetric high-order integration scheme for improved training on sparse and noisy data.

翻译：基于汉密尔顿式配方的混合机学习最近成功地展示了简单的机械系统。在这项工作中,我们用若干内部和外部港口,包括多辆相关坦克的系统,对简单的大规模循环系统和更为复杂和现实的系统,对这种方法进行压力测试,对各种条件下的性能进行量化,并表明采用不同的假设对性能产生很大影响,突出该方法的优点和局限性。我们证明港口-汉堡神经网络可以扩展到国家依赖的港口的更高层面。我们考虑学习已知和未知外部港口的系统。港口-哈米尔顿式配方可以发现偏差,在消除偏差时仍然提供一个有效的模型。最后,我们提议采用一个对称高顺序集成计划,以改进关于稀杂杂乱无遗的数据的培训。