Related papers: On Dynamic Mode Decomposition: Theory and Applicat…
Operational forecasting centers are investing in decadal (1-10 year) forecast systems to support long-term decision making for a more climate-resilient society. One method that has previously been employed is the Dynamic Mode Decomposition…
Dynamic Mode Decomposition (DMD) yields a linear, approximate model of a system's dynamics that is built from data. We seek to reduce the order of this model by identifying a reduced set of modes that best fit the output. We adopt a model…
A theoretic framework for dynamics is obtained by transferring dynamics from state space to its dual space. As a result, the linear structure where dynamics are analytically decomposed to subcomponents and invariant subspaces decomposition…
Simulating the dynamics of a nonequilibrium quantum many-body system by computing the two-time Green's function associated with such a system is computationally challenging. However, we are often interested in the time diagonal of such a…
Noise fundamentally limits the performance and predictive capabilities of classical and quantum dynamical systems by degrading stability and obscuring intrinsic dynamical characteristics. Characterizing such noise accurately is essential…
Aero-optical beam control relies on the development of low-latency forecasting techniques to quickly predict wavefronts aberrated by the Turbulent Boundary Layer (TBL) around an airborne optical system, and its study applies to a…
Extended dynamic mode decomposition (EDMD) is a data-driven algorithm for approximating spectral data of the Koopman operator associated to a dynamical system, combining a Galerkin method of order N and collocation method of order M.…
Koopman Mode Decomposition (KMD) is a technique of nonlinear time-series analysis that originates from point spectrum of the Koopman operator defined for an underlying nonlinear dynamical system. We present a numerical algorithm of KMD…
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…
Koopman operators linearize nonlinear dynamical systems, making their spectral information of crucial interest. Numerous algorithms have been developed to approximate these spectral properties, and Dynamic Mode Decomposition (DMD) stands…
This paper proposes Koopman operator theory and the related algorithm dynamical mode decomposition (DMD) for analysis and control of signalized traffic flow networks. DMD provides a model-free approach for representing complex oscillatory…
Koopman operators globally linearize nonlinear dynamical systems and their spectral information is a powerful tool for the analysis and decomposition of nonlinear dynamical systems. However, Koopman operators are infinite-dimensional, and…
Extended dynamic mode decomposition (EDMD) is a powerful tool to construct linear predictors of nonlinear dynamical systems by approximating the action of the Koopman operator on a subspace spanned by finitely many observable functions.…
Nonlinear dynamical systems with symmetries exhibit a rich variety of behaviors, including complex attractor-basin portraits and enhanced and suppressed bifurcations. Symmetry arguments provide a way to study these collective behaviors and…
Understanding nonlinear dynamical systems (NLDSs) is challenging in a variety of engineering and scientific fields. Dynamic mode decomposition (DMD), which is a numerical algorithm for the spectral analysis of Koopman operators, has been…
We present a novel reduced-order fluid simulation technique leveraging Dynamic Mode Decomposition (DMD) to achieve fast, memory-efficient, and user-controllable subspace simulation. We demonstrate that our approach combines the strengths of…
We present a low-rank Koopman operator formulation for accelerating deformable subspace simulation. Using a Dynamic Mode Decomposition (DMD) parameterization of the Koopman operator, our method learns the temporal evolution of deformable…
Dynamic mode decomposition (DMD) provides a regression framework for adaptively learning a best-fit linear dynamics model over snapshots of temporal, or spatio-temporal, data. A diversity of regression techniques have been developed for…
Dynamic mode decomposition (DMD) is a data-driven technique widely used to analyze and model fluid problems including transonic buffet flows. Despite its strengths, DMD is known to suffer from sensitivities to the selected settings and the…
In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace. The Koopman operator is an infinite-dimensional linear operator that evolves…