Data-Driven Reduced-Order Models for Port-Hamiltonian Systems with Operator Inference

TL;DR

This paper extends Hamiltonian operator inference to port-Hamiltonian systems, enabling data-driven, structure-preserving reduced-order models that incorporate energy dissipation and external inputs, with hyper-reduction for efficiency and error estimates for accuracy.

Contribution

The work introduces a novel data-driven framework for port-Hamiltonian systems that preserves structure, includes hyper-reduction, and provides error analysis, extending previous Hamiltonian inference methods.

Findings

Successfully preserves system structure in reduced models.

Achieves accurate approximations validated on numerical examples.

Reduces computational complexity via hyper-reduction.

Abstract

Hamiltonian operator inference has been developed in [Sharma, H., Wang, Z., Kramer, B., Physica D: Nonlinear Phenomena, 431, p.133122, 2022] to learn structure-preserving reduced-order models (ROMs) for Hamiltonian systems. The method constructs a low-dimensional model using only data and knowledge of the functional form of the Hamiltonian. The resulting ROMs preserve the intrinsic structure of the system, ensuring that the mechanical and physical properties of the system are maintained. In this work, we extend this approach to port-Hamiltonian systems, which generalize Hamiltonian systems by including energy dissipation, external input, and output. Based on snapshots of the system's state and output, together with the information about the functional form of the Hamiltonian, reduced operators are inferred through optimization and are then used to construct data-driven ROMs. To further alleviate the complexity of evaluating nonlinear terms in the ROMs, a hyper-reduction method via discrete empirical interpolation is applied. Accordingly, we derive error estimates for the ROM approximations of the state and output. Finally, we demonstrate the structure preservation, as well as the accuracy of the proposed port-Hamiltonian operator inference framework, through numerical experiments on a linear mass-spring-damper problem and a nonlinear Toda lattice problem.