# Data-driven identification of port-Hamiltonian DAE systems by Gaussian processes

arXiv: https://arxiv.org/abs/2406.18726 · HTML: https://mlsanity.com/paper/2406.18726/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 22 references that are in the map.
- First posted on arXiv 26 Jun 2024.

## Builds on (most cited first, 12 of 12)

- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [DAE-PINN: A Physics-Informed Neural Network Model for Simulating Differential-Algebraic Equations with Application to Power Networks](https://mlsanity.com/paper/2109.04304/) (2021)
- [Symplectic Gaussian Process Regression of Hamiltonian Flow Maps](https://mlsanity.com/paper/2009.05569/) (2020)
- [Gaussian Process Port-Hamiltonian Systems: Bayesian Learning with Physics Prior](https://mlsanity.com/paper/2305.09017/) (2023)
- [Port-Hamiltonian Dynamic Mode Decomposition](https://mlsanity.com/paper/2204.13474/) (2022)
- [A Non-Intrusive Method to Inferring Linear Port-Hamiltonian Realizations using Time-Domain Data](https://mlsanity.com/paper/2005.09371/) (2020)
- [Numerical methods to compute a minimal realization of a port-Hamiltonian system](https://mlsanity.com/paper/1903.07042/) (2019)
- [Structure-preserving discretization for port-Hamiltonian descriptor systems](https://mlsanity.com/paper/1903.10451/) (2019)
- [Identification of Port-Hamiltonian Systems from Frequency Response Data](https://mlsanity.com/paper/1911.00080/) (2019)
- [Port-Hamiltonian System Identification from Noisy Frequency Response Data](https://mlsanity.com/paper/2106.11355/) (2021)
- [Learning Data-Driven PCHD Models for Control Engineering Applications](https://mlsanity.com/paper/2204.09436/) (2022)
- [Data-driven adjoint-based calibration of port-Hamiltonian systems in time domain](https://mlsanity.com/paper/2301.03924/) (2023)

## Built on by (most cited first, 2 of 2)

- [Data-driven identification of latent port-Hamiltonian systems](https://mlsanity.com/paper/2408.08185/) (2024)
- [Learning Passive Continuous-Time Dynamics with Multistep Port-Hamiltonian Gaussian Processes](https://mlsanity.com/paper/2510.00384/) (2025)

## Abstract (arXiv)

Port-Hamiltonian systems (pHS) allow for a structure-preserving modeling of dynamical systems. Coupling pHS via linear relations between input and output defines an overall pHS, which is structure preserving. However, in multiphysics applications, some subsystems do not allow for a physical pHS description, as (a) this is not available or (b) too expensive. Here, data-driven approaches can be used to deliver a pHS for such subsystems, which can then be coupled to the other subsystems in a structure-preserving way. In this work, we derive a data-driven identification approach for port-Hamiltonian differential algebraic equation (DAE) systems. The approach uses input and state space data to estimate nonlinear effort functions of pH-DAEs. As underlying technique, we us (multi-task) Gaussian processes. This work thereby extends over the current state of the art, in which only port-Hamiltonian ordinary differential equation systems could be identified via Gaussian processes. We apply this approach successfully to two applications from network design and constrained multibody system dynamics, based on pH-DAE system of index one and three, respectively.