SIPHy: Sparse identification of port-Hamiltonian systems from noisy data
Abstract
We propose sparse identification of port-Hamiltonian systems (SIPHy), enabling structure-preserving symbolic regression from noisy trajectory observations. The method applies to port-Hamiltonian systems, which provide a general framework for describing dynamical systems in terms of energy exchange, dissipation and control. Our algorithm can jointly identify the Hamiltonian as well as the dissipation and input matrices. Furthermore, we introduce Hamiltonian flow splines to better approximate derivatives of trajectory data corrupted by noise or with missing time points, a major challenge of system identification for differential equations. This method assembles flows of piecewise polynomial Hamiltonians to produce a smooth, differentiable trajectory necessary for sparse regression. Combining flow splines with SIPHy yields interpretable, physically grounded models from noisy and incomplete trajectory data. Because the Hamiltonian, dissipation, and input matrices are identified as separate components, the resulting models can be simulated under control inputs and dissipation regimes never observed during training, thus improving the robustness and generalization capabilities of model discovery methods.
Related
- Structure-Preserving Data-Driven Identification of Port-Hamiltonian Differential-Algebraic Systems
- Nonlocal Hamiltonian Dynamics on Sparse Lévy Graphs: Spectral Analysis and Multimodal Sampling
- Universal classical and quantum fluctuations in the large deviations of current of noisy quantum systems: Quantum symmetric simple exclusion and inclusion processes
- On Convergence Behavior of Randomized Kaczmarz-type Methods for Solving Doubly Noisy Linear Systems
- Explicit Criteria for Finite-Time Identification in Sparse Primal--Dual Dynamics
BibTeX
@misc{myhr2026siphy,
title = {{SIPHy: Sparse identification of port-Hamiltonian systems from noisy data}},
author = {Håkon Noren Myhr and Sølve Eidnes and J. Nathan Kutz},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20399},
eprint = {2609.20399},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20399},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - SIPHy: Sparse identification of port-Hamiltonian systems from noisy data
AU - Håkon Noren Myhr
AU - Sølve Eidnes
AU - J. Nathan Kutz
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.20399
UR - https://arxiv.org/abs/2609.20399
AB - We propose sparse identification of port-Hamiltonian systems (SIPHy), enabling structure-preserving symbolic regression from noisy trajectory observations. The method applies to port-Hamiltonian systems, which provide a general framework for describing dynamical systems in terms of energy exchange, dissipation and control. Our algorithm can jointly identify the Hamiltonian as well as the dissipation and input matrices. Furthermore, we introduce Hamiltonian flow splines to better approximate derivatives of trajectory data corrupted by noise or with missing time points, a major challenge of system identification for differential equations. This method assembles flows of piecewise polynomial Hamiltonians to produce a smooth, differentiable trajectory necessary for sparse regression. Combining flow splines with SIPHy yields interpretable, physically grounded models from noisy and incomplete trajectory data. Because the Hamiltonian, dissipation, and input matrices are identified as separate components, the resulting models can be simulated under control inputs and dissipation regimes never observed during training, thus improving the robustness and generalization capabilities of model discovery methods.
ER -