# Model-free system identification of surface ships in waves via Hankel dynamic mode decomposition with control

arXiv: https://arxiv.org/abs/2502.15782 · HTML: https://mlsanity.com/paper/2502.15782/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 82 references that are in the map.
- First posted on arXiv 17 Feb 2025.

## Builds on (most cited first, 11 of 11)

- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Modern Koopman Theory for Dynamical Systems](https://mlsanity.com/paper/2102.12086/) (2021)
- [Learning Koopman Invariant Subspaces for Dynamic Mode Decomposition](https://mlsanity.com/paper/1710.04340/) (2017)
- [Linearly-Recurrent Autoencoder Networks for Learning Dynamics](https://mlsanity.com/paper/1712.01378/) (2017)
- [Dynamic mode decomposition with control](https://mlsanity.com/paper/1409.6358/) (2014)
- [Generalizing Koopman Theory to allow for inputs and control](https://mlsanity.com/paper/1602.07647/) (2016)
- [Extracting spatial-temporal coherent patterns in large-scale neural recordings using dynamic mode decomposition](https://mlsanity.com/paper/1409.5496/) (2014)
- [Model-free, Model-based, and General Intelligence](https://mlsanity.com/paper/1806.02308/) (2018)
- [Learning functionals via LSTM neural networks for predicting vessel dynamics in extreme sea states](https://mlsanity.com/paper/1912.13382/) (2019)
- [Stochastically forced ensemble dynamic mode decomposition for forecasting and analysis of near-periodic systems](https://mlsanity.com/paper/2010.04248/) (2020)
- [Predicting Ship Responses in Different Seaways using a Generalizable Force Correcting Machine Learning Method](https://mlsanity.com/paper/2405.08033/) (2024)

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

- [System Identification of a Moored ASV with Recessed Moon Pool via Deterministic and Bayesian Hankel-DMDc](https://mlsanity.com/paper/2511.03482/) (2025)
- [Data-driven uncertainty-aware seakeeping prediction of the Delft 372 catamaran using ensemble Hankel dynamic mode decomposition](https://mlsanity.com/paper/2511.04461/) (2025)

## Abstract (arXiv)

This study introduces and compares the Hankel dynamic mode decomposition with control (Hankel-DMDc) and a novel Bayesian extension of Hankel-DMDc as model-free (i.e., data-driven and equation-free) approaches for system identification and prediction of free-running ship motions in irregular waves. The proposed DMDc methods create a reduced-order model using limited data from the system state and incoming wave elevation histories, with the latter and rudder angle serving as forcing inputs. The inclusion of delayed states of the system as additional dimensions per the Hankel-DMDc improves the representation of the underlying non-linear dynamics of the system by DMD. The approaches are statistically assessed using data from free-running simulations of a 5415M hull's course-keeping in irregular beam-quartering waves at sea state 7, a highly severe condition characterized by nonlinear responses near roll-resonance. The results demonstrate robust performance and remarkable computational efficiency. The results indicate that the proposed methods effectively identify the dynamic system in analysis. Furthermore, the Bayesian formulation incorporates uncertainty quantification and enhances prediction accuracy. Ship motions are predicted with good agreement with test data over a 15 encounter waves observation window. No significant accuracy degradation is noted along the test sequences, suggesting the method can support accurate and efficient maritime design and operational planning.