# Equation-Free Digital Twins for Nonlinear Structural Dynamics

arXiv: https://arxiv.org/abs/2605.00950 · HTML: https://mlsanity.com/paper/2605.00950/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 54 references that are in the map.
- First posted on arXiv 1 May 2026.

## Builds on (most cited first, 9 of 9)

- [Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control](https://mlsanity.com/paper/1611.03537/) (2016)
- [Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations](https://mlsanity.com/paper/2407.07218/) (2024)
- [Grey-box models for wave loading prediction](https://mlsanity.com/paper/2105.13813/) (2021)
- [Deep Operator Learning for High-Fidelity Fluid Flow Field Reconstruction from Sparse Sensor Measurements](https://mlsanity.com/paper/2412.08009/) (2024)
- [Dynamic mode decomposition for compressive system identification](https://mlsanity.com/paper/1710.07737/) (2017)
- [Easy attention: A simple attention mechanism for temporal predictions with transformers](https://mlsanity.com/paper/2308.12874/) (2023)
- [Analysis, forecasting and system identification of a floating offshore wind turbine using dynamic mode decomposition](https://mlsanity.com/paper/2411.07263/) (2024)
- [Data-Assimilated Model-Based Reinforcement Learning for Partially Observed Chaotic Flows](https://mlsanity.com/paper/2504.16588/) (2025)
- [A Mechanistic Analysis of Transformers for Dynamical Systems](https://mlsanity.com/paper/2512.21113/) (2025)

## Abstract (arXiv)

Monitoring high-dimensional engineering structures in extreme environments is limited by non-stationary excitation, nonlinear structural kinematics, and stochastic forcing. Traditional model-based and black-box data-driven methods often struggle to resolve these dynamics in real time, particularly under sensor failure or partial observability. This paper introduces a rank-optimized digital twin framework based on Koopman operator theory, Hankel-matrix embeddings, and dynamic mode decomposition. By lifting operational data into a linear invariant subspace, the method enables autonomous, input-blind reconstruction of structural states without requiring a priori mass or stiffness matrices. The framework is validated on an NREL 5MW spar-buoy floating offshore wind turbine, representing a challenging coupled aero-hydro-servo-elastic system. Results show that the rank-optimized Koopman-Hankel manifold separates structural resonances from deterministic 3P rotor harmonics under colored noise, where standard subspace identification can be unreliable. A rolling-horizon virtual sensing strategy achieves high-fidelity reconstruction at critical structural hotspots, with coefficient of determination greater than 0.95 at 1 Hz data assimilation and accuracy exceeding 0.99 at higher sampling rates. By estimating a physical Lyapunov time of approximately 1.0 s, the study defines the predictability horizon associated with the system information barrier. The proposed framework provides a computationally efficient and resilient digital twin approach for real-time identification and virtual sensing of complex structural dynamics.