Related papers: Dynamic Mode Decomposition and Koopman Theory
The Distributional Koopman Operator (DKO) is introduced as a way to perform Koopman analysis on random dynamical systems where only aggregate distribution data is available, thereby eliminating the need for particle tracking or detailed…
When complex systems with nonlinear dynamics achieve an output performance objective, only a fraction of the state dynamics significantly impacts that output. Those minimal state dynamics can be identified using the differential geometric…
The scientific computation methods development in conjunction with artificial intelligence technologies remains a hot research topic. Finding a balance between lightweight and accurate computations is a solid foundation for this direction.…
Extended Dynamic Mode Decomposition (EDMD) is an algorithm that approximates the action of the Koopman operator on an $N$-dimensional subspace of the space of observables by sampling at $M$ points in the state space. Assuming that the…
Extended Dynamic Mode Decomposition (EDMD) is a popular data-driven method to approximate the action of the Koopman operator on a linear function space spanned by a dictionary of functions. The accuracy of EDMD model critically depends on…
The modeling of nonlinear dynamics based on Koopman operator theory, which is originally applicable only to autonomous systems with no control, is extended to non-autonomous control system without approximation to input matrix B. Prevailing…
Construction of reduced-order models (ROMs) for hyperbolic conservation laws is notoriously challenging mainly due to the translational property and nonlinearity of the governing equations. While the Lagrangian framework for ROM…
Dynamic mode decomposition (DMD) is a widely used data-driven algorithm for predicting the future states of dynamical systems. However, its standard formulation often struggles with poor long-term predictive accuracy. To address this…
Residual Dynamic Mode Decomposition (ResDMD) offers a method for accurately computing the spectral properties of Koopman operators. It achieves this by calculating an infinite-dimensional residual from snapshot data, thus overcoming issues…
We apply Dynamic Mode Decomposition (DMD) to Elementary Cellular Automata (ECA). Three types of DMD methods are considered and the reproducibility of the system dynamics and Koopman eigenvalues from observed time series are investigated.…
We present an extension of optimal mode decomposition (OMD) for autonomous systems to systems with controls. The extension is developed along the same lines as the extension of dynamic mode decomposition (DMD) to DMD with control (DMDc).…
The Koopman operator provides a principled framework for analyzing nonlinear dynamical systems through linear operator theory. Recent advances in dynamic mode decomposition (DMD) have shown that trajectory data can be used to identify…
Human interpretation of the world encompasses the use of symbols to categorize sensory inputs and compose them in a hierarchical manner. One of the long-term objectives of Computer Vision and Artificial Intelligence is to endow machines…
We present parameter-interpolated dynamic mode decomposition (piDMD), a parametric reduced-order modeling framework that embeds known parameter-affine structure directly into the DMD regression step. Unlike existing parametric DMD methods…
A popular technique used to obtain linear representations of nonlinear systems is the so-called Koopman approach, where the nonlinear dynamics are lifted to a (possibly infinite dimensional) linear space through nonlinear functions called…
A numerical framework is proposed for identifying partial differential equations (PDEs) governing dynamical systems directly from their observation data using Chebyshev polynomial approximation. In contrast to data-driven approaches such as…
This paper develops a novel data-driven technique to compute the participation factors for nonlinear systems based on the Koopman mode decomposition. Provided that certain conditions are satisfied, it is shown that the proposed technique…
We revisit the setting and the assumptions that underlie the methodology of Dynamic Mode Decomposition (DMD) in order to highlight caveats as well as potential measures of when the applicability is warranted.
The eigenspectrum of the Koopman operator enables the decomposition of nonlinear dynamics into a sum of nonlinear functions of the state space with purely exponential and sinusoidal time dependence. For a limited number of dynamical…
Nonlinear differential equations are encountered as models of fluid flow, spiking neurons, and many other systems of interest in the real world. Common features of these systems are that their behaviors are difficult to describe exactly and…