# Kernel learning for robust dynamic mode decomposition: linear and nonlinear disambiguation optimization

@article{Baddoo2021KernelLF, title={Kernel learning for robust dynamic mode decomposition: linear and nonlinear disambiguation optimization}, author={Peter J. Baddoo and Benjamin Herrmann and Beverley J. McKeon and Steven L. Brunton}, journal={Proceedings. Mathematical, Physical, and Engineering Sciences}, year={2021}, volume={478} }

Research in modern data-driven dynamical systems is typically focused on the three key challenges of high dimensionality, unknown dynamics and nonlinearity. The dynamic mode decomposition (DMD) has emerged as a cornerstone for modelling high-dimensional systems from data. However, the quality of the linear DMD model is known to be fragile with respect to strong nonlinearity, which contaminates the model estimate. By contrast, sparse identification of nonlinear dynamics learns fully nonlinear…

## 14 Citations

### Operator inference for non-intrusive model reduction with quadratic manifolds

- Computer Science, MathematicsComputer Methods in Applied Mechanics and Engineering
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### Physics-informed dynamic mode decomposition (piDMD)

- Computer ScienceArXiv
- 2021

In this work, we demonstrate how physical principles – such as symmetries, invariances, and conservation laws – can be integrated into the dynamic mode decomposition (DMD). DMD is a widely-used data…

### Residual dynamic mode decomposition: robust and verified Koopmanism

- PhysicsJournal of Fluid Mechanics
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Abstract Dynamic mode decomposition (DMD) describes complex dynamic processes through a hierarchy of simpler coherent features. DMD is regularly used to understand the fundamental characteristics of…

### Stabilized Neural Ordinary Differential Equations for Long-Time Forecasting of Dynamical Systems

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### Dynamic mode decomposition in adaptive mesh refinement and coarsening simulations

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This paper proposes a strategy to enable DMD to extract features from observations with different mesh topologies and dimensions, such as those found in AMR/C simulations, and evaluates DMD’s ability to extrapolate in time (short-time future estimates).

### Rigorous data-driven computation of spectral properties of Koopman operators for dynamical systems

- Computer Science, MathematicsArXiv
- 2021

Data-driven algorithms with rigorous convergence guarantees for computing spectral information of Koopman operators from trajectory data are described, which can achieve high-order convergence even for chaotic systems, when computing the density of the continuous spectrum and the discrete spectrum.

### Ensemble forecasts in reproducing kernel Hilbert space family: dynamical systems in Wonderland

- MathematicsSSRN Electronic Journal
- 2022

A methodological framework for ensemble-based estimation and simulation of high dimensional dynamical systems such as the oceanic or atmospheric flows is proposed. To that end, the dynamical system…

### Incremental Low-Rank Dynamic Mode Decomposition Model for Efficient Forecast Dissemination and Onboard Forecasting

- Computer ScienceOCEANS 2022, Hampton Roads
- 2022

In the MAR region, the incremental Low-Rank Dynamic Mode Decomposition (iLRDMD) models are sufficiently accurate and efficient for onboard ocean and acoustic forecasting of temperature, salinity, velocity, and transmission loss fields.

### Data-driven Acceleration of Quantum Optimization and Machine Learning via Koopman Operator Learning

- Computer Science, Physics
- 2022

This paper proposes a data-driven approach for accelerating quantum optimization and machine learning via Koopman operator learning and develops new methods including the sliding window dynamic mode decomposition (DMD) and the neural-network-based DMD to predict parameter updates on quantum computers.

### Koopman Operator learning for Accelerating Quantum Optimization and Machine Learning

- Computer Science, PhysicsArXiv
- 2022

This paper proposes a data-driven approach using Koopman operator learning to accelerate quantum optimization and quantum machine learning and develops two new families of methods: the sliding window dynamic mode decomposition (DMD) and the neural DMD for efficiently updating parameters on quantum computers.

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