相关论文: On the Effect of Quantization on Dynamic Mode Deco…

Koopman analysis provides a general framework from which to analyze a nonlinear dynamical system in terms of a linear operator acting on an infinite-dimensional observable space. This theoretical framework provides a rigorous underpinning…

Dynamical decoupling (DD) is a widely-used quantum control technique that takes advantage of temporal symmetries in order to partially suppress quantum errors without the need resource-intensive error detection and correction protocols.…

The dynamic mode decomposition (DMD) is a data-driven approach that extracts the dominant features from spatiotemporal data. In this work, we introduce sparse-mode DMD, a new variant of the optimized DMD framework that specifically…

Dataset Distillation (DD) compresses large datasets into compact synthetic ones that maintain training performance. However, current methods mainly target sample reduction, with limited consideration of data precision and its impact on…

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.…

Dynamic Mode Decomposition (DMD) is a powerful, data-driven method for diagnosing complex dynamics. Various DMD algorithms allow one to fit data with a low-rank model that decomposes it into a sum of coherent spatiotemporal patterns.…

We study the convergence of Hermitian Dynamic Mode Decomposition (DMD) to the spectral properties of self-adjoint Koopman operators. Hermitian DMD is a data-driven method that approximates the Koopman operator associated with an unknown…

We present a data-efficient algorithm for learning models for model-predictive control (MPC). Our approach, Jacobian-Regularized Dynamic-Mode Decomposition (JDMD), offers improved sample efficiency over traditional Koopman approaches based…

We derive a data-driven method for the approximation of the Koopman generator called gEDMD, which can be regarded as a straightforward extension of EDMD (extended dynamic mode decomposition). This approach is applicable to deterministic and…

This work continues the parametric investigation on the sampling nuances of the Dynamic Mode Decomposition (DMD) under the Koopman analysis. Through turbulent wakes, the investigation corroborated the generality of the universal convergence…

We present Latent Diffeomorphic Dynamic Mode Decomposition (LDDMD), a new data reduction approach for the analysis of non-linear systems that combines the interpretability of Dynamic Mode Decomposition (DMD) with the predictive power of…

Dynamical sampling deals with signals that evolve in time under the action of a linear operator. The purpose of the present paper is to analyze the performance of the basic dynamical sampling algorithms in the finite dimensional case and…

Dynamic Mode Decomposition (DMD) is a data-driven and model-free decomposition technique. It is suitable for revealing spatio-temporal features of both numerically and experimentally acquired data. Conceptually, DMD performs a…

Dynamic mode decomposition (DMD) is an efficient tool for decomposing spatio-temporal data into a set of low-dimensional modes, yielding the oscillation frequencies and the growth rates of physically significant modes. In this paper, we…

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…

In this two-part article, we evaluate the utility and the generalizability of the Dynamic Mode Decomposition (DMD) algorithm for data-driven analysis and reduced-order modelling of plasma dynamics in cross-field ExB configurations. The DMD…

The growing scale of large language models (LLMs) not only demands extensive computational resources but also raises environmental concerns due to their increasing carbon footprint. Model quantization emerges as an effective approach that…

We present a data-driven method for separating complex, multiscale systems into their constituent time-scale components using a recursive implementation of dynamic mode decomposition (DMD). Local linear models are built from windowed…

Balanced data is required for deep neural networks (DNNs) when learning to perform power system stability assessment. However, power system measurement data contains relatively few events from where power system dynamics can be learnt. To…

The Koopman operator is a mathematical tool that allows for a linear description of non-linear systems, but working in infinite dimensional spaces. Dynamic Mode Decomposition and Extended Dynamic Mode Decomposition are amongst the most…