Learning Subsystem Dynamics in Nonlinear Systems via Port-Hamiltonian Neural Networks

TL;DR

An algorithm is developed that learns the dynamics of individual subsystems, without requiring direct access to their internal states, without requiring direct access to their internal states by utilizing the inherent compositional property of the port-Hamiltonian systems.

Abstract

Port-Hamiltonian neural networks (pHNNs) are emerging as a powerful modeling tool that integrates physical laws with deep learning techniques. While most research has focused on modeling the entire dynamics of interconnected systems, the potential for identifying and modeling individual subsystems while operating as part of a larger system has been overlooked. This study addresses this gap by introducing a novel method for using pHNNs to identify such subsystems based solely on input-output measurements. By utilizing the inherent compositional property of the port-Hamiltonian systems, we developed an algorithm that learns the dynamics of individual subsystems, without requiring direct access to their internal states. On top of that, by choosing an output error (OE) model structure, we have been able to handle measurement noise effectively. The effectiveness of the proposed approach is demonstrated through tests on interconnected systems, including multi-physics scenarios, demonstrating its potential for identifying subsystem dynamics and facilitating their integration into new interconnected models.

Figures (7)

• Figure 1: Motivation of the paper: learning the dynamics of a subsystem within one interconnected system such that it remains a valid model when the subsystem is part of another larger system.
• Figure 2: Schematic overview of the model structure for a composite system consisting of two subsystems. Note that the ODE-Solver step can be repeated for multiple timesteps to simulate further into the future. For the experiments in this paper, a neural network is used for the encoder, but different options are possible.
• Figure 3: Schematic view of the three coupled mass-spring-dampers. For this system, the input is given as a force $u_{1}(t)$, the states are the displacements, ${q}(t)$, and momenta, ${p}(t)$, of the masses, while the outputs are the velocities of the masses $\dot{{q}}(t)$. Note that this can be viewed as a single composite system, or as three interacting subsystems.
• Figure 4: Example of the three MSD system behavior for the first 100 seconds. The first subplot shows the external force that is taken as an input, $u_1$. The second subplot shows the corresponding output measurements of the velocities of the three masses, $y$.
• Figure 5: Simulation of the identified model for the first 100 seconds. In the first subplot, the dots represent the sampled true output values, while the solid lines indicate the simulation response of the model. The second subplot shows the error between the simulated and measured outputs. The amplitude of the noise is indicated with the dashed lines.