Related papers: A tensor-based dynamic mode decomposition based on…

Dynamic mode decomposition (DMD) is a powerful and increasingly popular tool for performing spectral analysis of fluid flows. However, it requires data that satisfy the Nyquist-Shannon sampling criterion. In many fluid flow experiments,…

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…

Modern approaches to generative modeling of continuous data using tensor networks incorporate compression layers to capture the most meaningful features of high-dimensional inputs. These methods, however, rely on traditional Matrix Product…

We propose a strategy to compress and store large volumes of scientific data represented on unstructured grids. Approaches utilizing tensor decompositions for data compression have already been proposed. Here, data on a structured grid is…

Model order reduction plays a crucial role in simplifying complex systems while preserving their essential dynamic characteristics, making it an invaluable tool in a wide range of applications, including robotic systems, signal processing,…

The transition kernel of a continuous-state-action Markov decision process (MDP) admits a natural tensor structure. This paper proposes a tensor-inspired unsupervised learning method to identify meaningful low-dimensional state and action…

The widespread use of multisensor technology and the emergence of big datasets have created the need to develop tools to reduce, approximate, and classify large and multimodal data such as higher-order tensors. While early approaches…

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…

Dynamic Mode Decomposition (DMD) describes complex dynamic processes through a hierarchy of simpler coherent features. DMD is regularly used to understand the fundamental characteristics of turbulence and is closely related to Koopman…

In this paper we propose novel methods for compression and recovery of multilinear data under limited sampling. We exploit the recently proposed tensor- Singular Value Decomposition (t-SVD)[1], which is a group theoretic framework for…

The time-dependent fields obtained by solving partial differential equations in two and more dimensions quickly overwhelm the analytical capabilities of the human brain. A meaningful insight into the temporal behaviour can be obtained by…

Dynamic mode decomposition (DMD) is an emerging methodology that has recently attracted computational scientists working on nonintrusive reduced order modeling. One of the major strengths that DMD possesses is having ground theoretical…

The paper introduces a reduced order model (ROM) for numerical integration of a dynamical system which depends on multiple parameters. The ROM is a projection of the dynamical system on a low dimensional space that is both problem-dependent…

This paper proposes a gray-box stability analysis mechanism based on data-driven dynamic mode decomposition (DMD) for commercial grid-tied power electronics converters with limited information on its control parameters and topology. By…

While the acquisition of time series has become more straightforward, developing dynamical models from time series is still a challenging and evolving problem domain. Within the last several years, to address this problem, there has been a…

We revisit the setting and the assumptions that underlie the methodology of Dynamic Mode Decomposition (DMD) in order to highlight caveats as well as potential measures of when the applicability is warranted.

In order to guarantee the safety of payload, crew, and structures, ships must exhibit good seakeeping, maneuverability, and structural-response performance, also when they operate in adverse weather conditions. In this context, the…

This paper presents unifying results for subspace identification (SID) and dynamic mode decomposition (DMD) for autonomous dynamical systems. We observe that SID seeks to solve an optimization problem to estimate an extended observability…

We study the problem of learning mixtures of linear dynamical systems (MLDS) from input-output data. The mixture setting allows us to leverage observations from related dynamical systems to improve the estimation of individual models.…

The Tucker decomposition, an extension of singular value decomposition for higher-order tensors, is a useful tool in analysis and compression of large-scale scientific data. While it has been studied extensively for static datasets, there…