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Dynamic mode decomposition (DMD) is a popular data-driven framework to extract linear dynamics from complex high-dimensional systems. In this work, we study the system identification properties of DMD. We first show that DMD is invariant…

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…

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…

Originally introduced in the fluid mechanics community, dynamic mode decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of nonlinear systems. However, existing DMD theory deals primarily with sequential time…

Time series forecasting remains a central challenge problem in almost all scientific disciplines. We introduce a novel load forecasting method in which observed dynamics are modeled as a forced linear system using Dynamic Mode Decomposition…

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…

High-resolution simulations of particle-based kinetic plasma models typically require a high number of particles and thus often become computationally intractable. This is exacerbated in multi-query simulations, where the problem depends on…

Photon-counting CT (PCCT) offers improved diagnostic performance through better spatial and energy resolution, but developing high-quality image reconstruction methods that can deal with these large datasets is challenging. Model-based…

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…

Dynamical systems are ubiquitous within science and engineering, from turbulent flow across aircraft wings to structural variability of proteins. Although some systems are well understood and simulated, scientific imaging often confronts…

Dynamic mode decomposition (DMD) and its variants have emerged as popular methods for the post-processing of fluid dynamics' simulations in order to visualize dominant coherent structures and to reduce the practical degrees of freedom to a…

Compact semiconductor device models are essential for efficiently designing and analyzing large circuits. However, traditional compact model development requires a large amount of manual effort and can span many years. Moreover, inclusion…

Accurate and efficient wave-optics simulation of partially coherent light transport systems is critical for the design of advanced optical systems, ranging from computational lithography to diffraction-limited storage rings (DLSR). However,…

Image denoising is a fundamental problem in computational photography, where achieving high perception with low distortion is highly demanding. Current methods either struggle with perceptual quality or suffer from significant distortion.…

This paper discusses the predictive capability of Dynamic Mode Decomposition (DMD) in the context of orbital mechanics. The focus is specifically on the Hankel variant of DMD which uses a stacked set of time-delayed observations for system…

Reliable numerical computation of quantum dynamics is a fundamental challenge when the long-ranged quantum entanglement plays essential roles as in the cases governed by quantum criticality in strongly correlated systems. Here we apply a…

Temporal or spatial structures are readily extracted from complex data by modal decompositions like Proper Orthogonal Decomposition (POD) or Dynamic Mode Decomposition (DMD). Subspaces of such decompositions serve as reduced order models…

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…

Dynamic mode decomposition (DMD) has emerged as a popular data-driven modeling approach to identifying spatio-temporal coherent structures in dynamical systems, owing to its strong relation with the Koopman operator. For dynamical systems…

Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. In a previous work [arXiv:2104.13962], we explored the use of Neural Ordinary Differential Equations (NODE) as…