Stochastically Forced Ensemble Dynamic Mode Decomposition for Forecasting and Analysis of Near-Periodic Systems

@article{Dylewsky2022StochasticallyFE,
  title={Stochastically Forced Ensemble Dynamic Mode Decomposition for Forecasting and Analysis of Near-Periodic Systems},
  author={Daniel Dylewsky and David A. Barajas-Solano and Tong Ma and Alexandre M. Tartakovsky and J. Nathan Kutz},
  journal={IEEE Access},
  year={2022},
  volume={10},
  pages={33440-33448}
}
Time series forecasting remains a central challenge problem in almost all scientific disciplines. We introduce a novel load forecasting method in which observed dynamics are modeled as a forced linear system using Dynamic Mode Decomposition (DMD) in time delay coordinates. Central to this approach is the insight that grid load, like many observables on complex real-world systems, has an “almost-periodic” character, i.e., a continuous Fourier spectrum punctuated by dominant peaks, which capture… 

Figures from this paper

O N THE USE OF DYNAMIC MODE DECOMPOSITION FOR TIME - SERIES FORECASTING OF SHIPS MANEUVERING IN WAVES
A statistical analysis on the use of dynamic mode decomposition (DMD) and its augmented variant, via state augmentation, as data-driven and equation-free modeling approach for the prediction of
On the use of dynamic mode decomposition for time-series forecasting of ships operating in waves
A data-driven and equation-free modeling approach for forecasting of trajectories, motions, and forces of ships in waves is presented, based on dynamic mode decomposition (DMD). A statistical

References

SHOWING 1-10 OF 93 REFERENCES
and a at
The xishacorene natural products are structurally unique apolar diterpenoids that feature a bicyclo[3.3.1] framework. These secondary metabolites likely arise from the well-studied, structurally
and D
  • Fasino, “Relationship between singular spectrum analysis and fourier analysis: Theory and application to the monitoring of volcanic activity,” Computers &Mathematics with Applications, vol. 60, no. 3, pp. 812–820
  • 2010
Principal Component Trajectories (PCT): Nonlinear dynamics as a superposition of time-delayed periodic orbits
TLDR
This paper presents a method for learning linear control models in delay coordinates while simultaneously discovering the corresponding exogeneous forcing signal in a fully unsupervised manner and extends the existing DMD with control (DMDc) algorithm to cases where a control signal is not known a priori.
From Fourier to Koopman: Spectral Methods for Long-term Time Series Prediction
TLDR
This work introduces an algorithm with similarities to the Fourier transform but which does not rely on periodicity assumptions, allowing for forecasting given potentially arbitrary sampling intervals, and extends this algorithm to handle nonlinearities by leveraging Koopman theory.
Introduction to the Koopman Operator in Dynamical Systems and Control Theory
This introductory chapter provides an overview of the Koopman operator framework. We present basic notions and definitions, including those related to the spectral properties of the operator. We also
and s
Electric Load and Power Forecasting Using Ensemble Gaussian Process Regression
TLDR
This work uses a synthetic data set describing a power grid with 700 buses and 134 generators over a 365-days period with data synthetically generated at an hourly rate to propose a new forecasting method for predicting load demand and generation scheduling.
Dynamic mode decomposition for multiscale nonlinear physics.
TLDR
An overview of the algorithm and its results on two example physical systems are presented, and some advantages and potential forecasting applications for the technique are discussed.
Probabilistic electric load forecasting: A tutorial review
...
...