Output Error Port-Hamiltonian Neural Network

Hamiltonian Neural Networks (HNNs) represent a promising class of physics-informed deep learning methods that leverage Hamiltonian theory as foundational knowledge within data-driven model learning with neural
networks. However, their direct application to engineering systems is often hindered by practical challenges, including the presence of external inputs, dissipation, and noisy measurements. This study introduces a novel framework that enhances the capabilities of HNNs to address these real-life factors. We integrate port Hamiltonian theory into the neural network structure, allowing for the inclusion of external inputs and dissipation, while mitigating the impact of measurement noise through an output-error (OE) model structure. The resulting port Hamiltonian neural networks (pHNNs) can be adapted to tackle data-driven modeling complex engineering systems with noisy measurements. Furthermore, we develop an extension of the subspace encoder approach (SUBNET) for identification of pHNNs, which efficiently approximates the complete simulation loss using short simulations on subsections of the data and an encoder function to predict initial states. By integrating SUBNET with pHNNs, we achieve robust and physics-driven data-based learning of complex engineering systems under noisy measurements. We demonstrate the effectiveness of our approach on engineering benchmarks, showing its potential as a powerful tool for modeling dynamic systems in real-world applications.