Related papers: Dynamic mode decomposition for compressive system …
Linear dimensionality reduction methods are commonly used to extract low-dimensional structure from high-dimensional data. However, popular methods disregard temporal structure, rendering them prone to extracting noise rather than…
Compressive sensing is a powerful technique for recovering sparse solutions of underdetermined linear systems, which is often encountered in uncertainty quantification analysis of expensive and high-dimensional physical models. We perform…
Large language models deliver strong generative performance but at the cost of massive parameter counts, memory use, and decoding latency. Prior work has shown that pruning and structured sparsity can preserve accuracy under substantial…
Providing efficient and accurate parametrizations for model reduction is a key goal in many areas of science and technology. Here we present a strong link between data-driven and theoretical approaches to achieving this goal. Formal…
A novel data-driven method of modal analysis for complex flow dynamics, termed as reduced-order variational mode decomposition (RVMD), has been proposed, combining the idea of the separation of variables and a state-of-the-art nonstationary…
This paper presents a new technique for norm-convergent dynamic mode decomposition of deterministic systems. The developed method utilizes recent results on singular dynamic mode decomposition where it is shown that by appropriate selection…
Extracting the latent underlying structures of complex nonlinear local and nonlocal flows is essential for their analysis and modeling. In this work, we attempt to provide a consistent framework through Koopman theory and its related…
The modal decomposition techniques of proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) have become a common method for analysing the spatio-temporal coherence of dynamical systems. In particular, these techniques…
Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…
A data-driven and equation-free approach is proposed and discussed to model ships maneuvers in waves, based on the dynamic mode decomposition (DMD). DMD is a dimensionality-reduction/reduced-order modeling method, which provides a linear…
We establish the convergence of a class of numerical algorithms, known as Dynamic Mode Decomposition (DMD), for computation of the eigenvalues and eigenfunctions of the infinite-dimensional Koopman operator. The algorithms act on data…
Koopman operator theory shows how nonlinear dynamical systems can be represented as an infinite-dimensional, linear operator acting on a Hilbert space of observables of the system. However, determining the relevant modes and eigenvalues of…
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…
The emergence of Dynamic Mode Decomposition (DMD) as a practical way to attempt a Koopman mode decomposition of a nonlinear PDE presents exciting prospects for identifying invariant sets and slowly decaying transient structures buried in…
Recent deep learning extensions in Koopman theory have enabled compact, interpretable representations of nonlinear dynamical systems which are amenable to linear analysis. Deep Koopman networks attempt to learn the Koopman eigenfunctions…
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…
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…
Reduced-order models have long been used to understand the behavior of nonlinear partial differential equations (PDEs). Naturally, reduced-order modeling techniques come at the price of computational accuracy for a decrease in computation…
Recently, we have demonstrated that our approach is a highly effective tool while analysing complex phenomena existing in networks of coupled nonlinear systems. In the present article we present the results of our investigations into a…
A data-driven analysis method known as dynamic mode decomposition (DMD) approximates the linear Koopman operator on projected space. In the spirit of Johnson-Lindenstrauss Lemma, we will use random projection to estimate the DMD modes in…