Data-driven identification of latent port-Hamiltonian systems

TL;DR

The paper addresses data-driven discovery of dynamical models that preserve physical structure by identifying port-Hamiltonian (pH) systems from high-dimensional data. It introduces two methods: pHIN, which learns a latent linear pH model directly, and ApHIN, which embeds autoencoder-based coordinates to handle nonlinear, high-dimensional data while enforcing pH structure in the latent space and transferring it to the physical space. The approach ensures passivity and Lyapunov stability in the latent domain and, under mild assumptions, in the reconstructed state space, demonstrated on a parametric mass-spring-damper, a nonlinear pendulum, and a high-dimensional disc brake FE model. The framework enables fast, structure-preserving reduced-order modeling suitable for multi-physics applications and control, with potential extensions to partial observations and constrained autoencoders for stronger guarantees. Overall, it advances non-intrusive, interpretable model discovery for energy-based systems and provides a scalable path to reliable, physics-consistent surrogates.

Abstract

Conventional physics-based modeling techniques involve high effort, e.g., time and expert knowledge, while data-driven methods often lack interpretability, structure, and sometimes reliability. To mitigate this, we present a data-driven system identification framework that derives models in the port-Hamiltonian (pH) formulation. This formulation is suitable for multi-physical systems while guaranteeing the useful system theoretical properties of passivity and stability. Our framework combines linear and nonlinear reduction with structured, physics-motivated system identification. In this process, high-dimensional state data obtained from possibly nonlinear systems serves as input for an autoencoder, which then performs two tasks: (i) nonlinearly transforming and (ii) reducing this data onto a low-dimensional latent space. In this space, a linear pH system, that satisfies the pH properties per construction, is parameterized by the weights of a neural network. The mathematical requirements are met by defining the pH matrices through Cholesky factorizations. The neural networks that define the coordinate transformation and the pH system are identified in a joint optimization process to match the dynamics observed in the data while defining a linear pH system in the latent space. The learned, low-dimensional pH system can describe even nonlinear systems and is rapidly computable due to its small size. The method is exemplified by a parametric mass-spring-damper and a nonlinear pendulum example, as well as the high-dimensional model of a disc brake with linear thermoelastic behavior.

Figures (8)

• Figure 1: Schematic illustration of the port-Hamiltonian identification network (pHIN). We denote dependency on the time step $t_i$ and parameter $\bm{\mu}_i$ as a subindex $(\cdot)_i$ for the sake of brevity.
• Figure 2: Schematic illustration of the ApHIN approach: An autoencoder composed of linear (PCA) and nonlinear (autoencoder) reduction identifies a low-dimensional manifold on which a linear pH system is identified on the latent space using our proposed pHIN approach. We denote dependency on the time step $t_i$ and parameter $\bm{\mu}_i$ as a subindex $(\cdot)_i$ for the sake of brevity.
• Figure 3: Model evaluation of the identified system: The identified (parametric) pH system is time-integrated using given inputs and the encoded initial conditions. Subsequently, the latent results are decoded into the high-dimensional space.
• Figure 4: A mass-spring-damper chain \ref{['fig:mass-spring-damper']} that serves as a simple mechanical example for the port-Hamiltonian identification framework. The corresponding identified system matrices can be seen in \ref{['fig:msd-matrices']}.
• Figure 5: Sketch of the mathematical pendulum (\ref{['fig:pendulum']}) along with the results of the pH identification (\ref{['fig: pendulum results']}).

Theorems & Definitions (6)

• Definition 1: Equilibrium Point and Lyapunov Stability, e.g., Meyer17
• Theorem 1: Lyapunov's Stability Theorem, e.g., Meyer17
• Theorem 2: Boundedness of Solutions
• Theorem 3
• proof
• proof