Related papers: Local Analysis of Dissipative Dynamical Systems
We apply the truncated singular value decomposition (SVD) to extract the underlying 2D correlation functions from small-angle scattering patterns. We test the approach by transforming the simulated data of ellipsoidal particles and show…
Singular Value Decomposition (SVD) is a powerful tool for multivariate analysis. However, independent computation of the SVD for each sample taken from a bandlimited matrix random process will result in singular value sample paths whose…
The development of the manufacturing systems has made it increasingly necessary to monitor the data generated by multiple interconnected subsystems with rapid incoming of samples. Based on incremental Singular Value Decomposition (ISVD), we…
We address the problem of data-driven pattern identification and outlier detection in time series. To this end, we use singular value decomposition (SVD) which is a well-known technique to compute a low-rank approximation for an arbitrary…
In this letter, we propose a simple yet effective singular value decomposition (SVD) based strategy to reduce the optimization problem dimension in data-enabled predictive control (DeePC). Specifically, in the case of linear time-invariant…
By singular value decomposition (SVD) of a numerically singular Hessian matrix and a numerically singular system of linear equations for the experimental data (accumulated in the respective ${\chi ^2}$ function) and constraints, least…
Modeling and predicting the dynamics of complex multiscale systems remains a significant challenge due to their inherent nonlinearities and sensitivity to initial conditions, as well as limitations of traditional machine learning methods…
Dynamic substructuring (DS) methods encompass a range of techniques to decompose large structural systems into multiple coupled subsystems. This decomposition has the principle benefit of reducing computational time for dynamic simulation…
Distributions measured in high energy physics experiments are usually distorted and/or transformed by various detector effects. A regularization method for unfolding these distributions is re-formulated in terms of the Singular Value…
Dissipativity is an input-output (IO) characterization of nonlinear systems that enables compositional robust control through Vidyasagar's Network Dissipativity Theorem (VDNT). However, determining the dissipativity of a system is an…
Dynamic Mode Decomposition (DMD) is a data-driven technique to identify a low dimensional linear time invariant dynamics underlying high-dimensional data. For systems in which such underlying low-dimensional dynamics is time-varying, a…
This work is concerned with the finite-horizon optimal covariance steering of networked systems governed by discrete-time stochastic linear dynamics. In contrast with existing work that has only considered systems with dynamically decoupled…
Surrogate testing techniques have been used widely to investigate the presence of dynamical nonlinearities, an essential ingredient of deterministic chaotic processes. Traditional surrogate testing subscribes to statistical hypothesis…
The evolution of images with physics-based dynamics is often spatially localized and nonlinear. A switching linear dynamic system (SLDS) is a natural model under which to pose such problems when the system's evolution randomly switches over…
Singular Value Decomposition (SVD) constitutes a bridge between the linear algebra concepts and multi-layer neural networks---it is their linear analogy. Besides of this insight, it can be used as a good initial guess for the network…
Singular value decomposition (SVD) is one of the most popular compression methods that approximate a target matrix with smaller matrices. However, standard SVD treats the parameters within the matrix with equal importance, which is a simple…
Time series measured from real-world systems are generally noisy, complex and display statistical properties that evolve continuously over time. Here, we present a method that combines wavelet analysis and non-stationary surrogates to…
Researchers in the behavioral and social sciences use linear discriminant analysis (LDA) for predictions of group membership (classification) and for identifying the variables most relevant to group separation among a set of continuous…
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…
Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…