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Dynamic Mode Decomposition (DMD) and its variants, such as extended DMD (EDMD), are broadly used to fit simple linear models to dynamical systems known from observable data. As DMD methods work well in several situations but perform poorly…
Reconstructing dynamic 4D scenes is an important yet challenging task. While 3D foundation models like VGGT excel in static settings, they often struggle with dynamic sequences where motion causes significant geometric ambiguity. To address…
Dynamic mode decomposition (DMD) is a data-driven method that models high-dimensional time series as a sum of spatiotemporal modes, where the temporal modes are constrained by linear dynamics. For nonlinear dynamical systems exhibiting…
The characterization of intermittent, multiscale and transient dynamics using data-driven analysis remains an open challenge. We demonstrate an application of the Dynamic Mode Decomposition (DMD) with sparse sampling for the diagnostic…
We introduce the method of compressed dynamic mode decomposition (cDMD) for background modeling. The dynamic mode decomposition (DMD) is a regression technique that integrates two of the leading data analysis methods in use today: Fourier…
To effectively address the issues of low sensitivity and high time consumption in time series anomaly detection, we propose an anomaly detection method based on cross-modal deep metric learning. A cross-modal deep metric learning feature…
Origami structures often serve as the building block of mechanical systems due to their rich static and dynamic behaviors. Experimental observation and theoretical modeling of origami dynamics have been reported extensively, whereas the…
Forecasting the short-term ridership among origin-destination pairs (OD matrix) of a metro system is crucial in real-time metro operation. However, this problem is notoriously difficult due to the high-dimensional, sparse, noisy, and skewed…
Spatial perception aims to estimate camera motion and scene structure from visual observations, a problem traditionally addressed through geometric modeling and physical consistency constraints. Recent learning-based methods have…
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…
Datasets such as images, text, or movies are embedded in high-dimensional spaces. However, in important cases such as images of objects, the statistical structure in the data constrains samples to a manifold of dramatically lower…
Proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are two complementary singular-value decomposition (SVD) techniques that are widely used to construct reduced-order models (ROMs) in a variety of fields of science…
The DMD (Dynamic Mode Decomposition) method has attracted widespread attention as a representative modal-decomposition method and can build a predictive model. However, the DMD may give predicted results that deviate from physical reality…
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…
We analyze the performance of Dynamic Mode Decomposition (DMD)-based approximations of the stochastic Koopman operator for random dynamical systems where either the dynamics or observables are affected by noise. For many DMD algorithms, the…
Accurate readout of low-power optical higher-order spatial modes is of increasing importance to the precision metrology community. Mode sensors are used to prevent mode mismatches from degrading quantum and thermal noise mitigation…
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 introduces a data-driven time embedding method for modeling long-range seasonal dependencies in spatiotemporal forecasting tasks. The proposed approach employs Dynamic Mode Decomposition (DMD) to extract temporal modes directly…
Signal decomposition (SD) approaches aim to decompose non-stationary signals into their constituent amplitude- and frequency-modulated components. This represents an important preprocessing step in many practical signal processing…
Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD)…