• Corpus ID: 244954605

Physics-informed dynamic mode decomposition (piDMD)

@article{Baddoo2021PhysicsinformedDM,
  title={Physics-informed dynamic mode decomposition (piDMD)},
  author={Peter J. Baddoo and Benjamin Herrmann and Beverley J. McKeon and J. Nathan Kutz and Steven L. Brunton},
  journal={ArXiv},
  year={2021},
  volume={abs/2112.04307}
}
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 analysis technique that extracts low-rank modal structures and dynamics from high-dimensional measurements. However, DMD frequently produces models that are sensitive to noise, fail to generalize outside the training data, and violate basic physical laws. Our physics-informed DMD (piDMD… 

Figures from this paper

Kernel learning for robust dynamic mode decomposition: linear and nonlinear disambiguation optimization
TLDR
This work presents a kernel method that learns interpretable data-driven models for high-dimensional, nonlinear systems and shows that it is possible to recover the linear model contribution with this approach, thus separating the effects of the implicitly defined nonlinear terms.
Port-Hamiltonian Dynamic Mode Decomposition
. We present a novel physics-informed system identification method to construct a passive linear time-invariant system. In more detail, for a given quadratic energy functional, measurements of the
Residual Dynamic Mode Decomposition: Robust and verified Koopmanism
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

References

SHOWING 1-10 OF 101 REFERENCES
Dynamic Mode Decomposition with Control
TLDR
This work develops a new method which extends dynamic mode decomposition (DMD) to incorporate the effect of control to extract low-order models from high-dimensional, complex systems and provides the additional innovation of being able to disambiguate between the underlying dynamics and the effects of actuation, resulting in accurate input-output models.
Physics-informed machine learning
TLDR
Some of the prevailing trends in embedding physics into machine learning are reviewed, some of the current capabilities and limitations are presented and diverse applications of physicsinformed learning both for forward and inverse problems, including discovering hidden physics and tackling highdimensional problems are discussed.
Kernel learning for robust dynamic mode decomposition: linear and nonlinear disambiguation optimization
TLDR
This work presents a kernel method that learns interpretable data-driven models for high-dimensional, nonlinear systems and shows that it is possible to recover the linear model contribution with this approach, thus separating the effects of the implicitly defined nonlinear terms.
On dynamic mode decomposition: Theory and applications
TLDR
A theoretical framework in which dynamic mode decomposition is defined as the eigendecomposition of an approximating linear operator, which generalizes DMD to a larger class of datasets, including nonsequential time series, and shows that under certain conditions, DMD is equivalent to LIM.
De-biasing the dynamic mode decomposition for applied Koopman spectral analysis of noisy datasets
TLDR
In the analysis of time-resolved particle image velocimetry data for a separated flow, TDMD outperforms standard DMD by providing dynamical interpretations that are consistent with alternative analysis techniques and extracts modes that reveal detailed spatial structures missed by standard D MD.
Characterizing and correcting for the effect of sensor noise in the dynamic mode decomposition
TLDR
It is shown analytically that DMD is biased to sensor noise, and how this bias depends on the size and noise level of the data is quantified.
Dynamic Mode Decomposition and Its Variants
  • P. Schmid
  • Biology
    Annual Review of Fluid Mechanics
  • 2021
TLDR
This review focuses on the practical aspects of DMD and its variants, as well as on its usage and characteristics as a quantitative tool for the analysis of complex fluid processes.
A dynamic mode decomposition approach for large and arbitrarily sampled systems
TLDR
This contribution presents an alternative algorithm to achieve Dynamic Mode Decomposition decomposition, overcoming the above-mentioned limitations.
Characterizing magnetized plasmas with dynamic mode decomposition
Accurate and efficient plasma models are essential to understand and control experimental devices. Existing magnetohydrodynamic or kinetic models are nonlinear, computationally intensive, and can be
Data-driven resolvent analysis
TLDR
This work develops a purely data-driven algorithm to perform resolvent analysis to obtain the leading forcing and response modes, without recourse to the governing equations, but instead based on snapshots of the transient evolution of linearly stable flows.
...
1
2
3
4
5
...