Related papers: On-the-fly algorithm for Dynamic Mode Decompositio…

We apply dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD) methods to flows in highly-heterogeneous porous media to extract the dominant coherent structures and derive reduced-order models via Galerkin projection.…

The incremental singular value decomposition (SVD) updates a truncated SVD as new columns arrive, replacing a single large SVD with a sequence of small ones. In floating-point arithmetic, each update multiplies the running singular basis by…

Accurate and efficient plasma models are essential to understand and control experimental devices. Existing magnetohydrodynamic or kinetic models are nonlinear, computationally intensive, and can be difficult to interpret, while often only…

Tactile Internet (TI) requires ultra-low latency and high reliability to ensure stability and transparency in touch-enabled teleoperation. However, variable delays and packet loss present significant challenges to maintaining immersive…

We formulate a low-storage method for performing dynamic mode decomposition that can be updated inexpensively as new data become available; this formulation allows dynamical information to be extracted from large datasets and data streams.…

Understanding and modeling complex dynamic systems is crucial for enhancing vehicle performance and safety, especially in the context of autonomous driving. Recently, popular methods such as Koopman operators and their approximators, known…

We introduce the optimized dynamic mode decomposition algorithm for constructing an adaptive and computationally efficient reduced order model and forecasting tool for global atmospheric chemistry dynamics. By exploiting a low-dimensional…

Training of deep neural networks (DNNs) frequently involves optimizing several millions or even billions of parameters. Even with modern computing architectures, the computational expense of DNN training can inhibit, for instance, network…

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…

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…

Low-rank decomposition, particularly Singular Value Decomposition (SVD), is a pivotal technique for mitigating the storage and computational demands of Large Language Models (LLMs). However, prevalent SVD-based approaches overlook the…

We introduce the Rigged Dynamic Mode Decomposition (Rigged DMD) algorithm, which computes generalized eigenfunction decompositions of Koopman operators. By considering the evolution of observables, Koopman operators transform complex…

The reconstruction and prediction of full-state flows from sparse data are of great scientific and engineering significance yet remain challenging, especially in applications where data are sparse and/or subjected to noise. To this end,…

The dynamic mode decomposition (DMD) is a data-driven method used for identifying the dynamics of complex nonlinear systems. It extracts important characteristics of the underlying dynamics using measured time-domain data produced either by…

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…

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…

We propose a new technique for obtaining reduced order models for nonlinear dynamical systems. Specifically, we advocate the use of the recently developed Dynamic Mode Decomposition (DMD), an equation-free method, to approximate the…

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…

This paper presents a machine-learning-enhanced longitudinal scanline method to extract vehicle trajectories from high-angle traffic cameras. The Dynamic Mode Decomposition (DMD) method is applied to extract vehicle strands by decomposing…

In this paper, we generalize the minimum flow decomposition problem (MFD) to incorporate uncertain edge capacities and tackle it from the perspective of robust optimization. In the classical flow decomposition problem, a network flow is…