Port-Hamiltonian Neural Networks for Learning Coupled Systems and Their Interactions

Recent advances in deep learning have shown its effectiveness in modeling physical phenomena, even when the governing equations are unknown. However, current studies mainly focus on mechanical systems, often overlooking other physical domains, such as electrical systems. Furthermore, existing methods tend to treat systems with multiple elements as a single entity, making it difficult to capture the complex interactions in coupled systems. To address these challenges, we propose a neural network framework based on the port-Hamiltonian formulation, which incorporates modularity and interactions between elements in the systems being modeled and is applicable to electrical circuits. Our experimental results demonstrate that our method is capable of handling various experimental scenarios that existing methods cannot address, while also improving modeling and prediction accuracy. Moreover, by analyzing the modeling results, we can identify the interactions between elements, providing interpretable results that facilitate understanding and further investigations.