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Singular value decomposition (SVD) is a standard matrix factorization technique that produces optimal low-rank approximations of matrices. It has diverse applications, including machine learning, data science and signal processing. However,…
Gradient based optimization methods are the established state-of-the-art paradigm to study strongly entangled quantum systems in two dimensions with Projected Entangled Pair States. However, the key ingredient, the gradient itself, has…
The Singular Value Decomposition (SVD) is one of the most important matrix factorizations, enjoying a wide variety of applications across numerous application domains. In statistics and data analysis, the common applications of SVD such as…
This paper presents a new method capable of reconstructing datasets with great precision and very low computational cost using a novel variant of the singular value decomposition (SVD) algorithm that has been named low-cost SVD (lcSVD).…
The tensor-train (TT) decomposition is widely used to compress large tensors into a more compact form by exploiting their inherent data structures. A fundamental approach for constructing the TT format is the well-known TT-SVD method, which…
Noise fundamentally limits the performance and predictive capabilities of classical and quantum dynamical systems by degrading stability and obscuring intrinsic dynamical characteristics. Characterizing such noise accurately is essential…
This paper evaluates Tucker decomposition and Singular Value Decomposition (SVD) for compressing neuroimaging data. Tucker decomposition preserves multi-dimensional relationships, achieving superior reconstruction fidelity and perceptual…
Dynamic Mode Decomposition (DMD) is a data-driven method for approximating the spatiotemporal modes of a system. The eigenvectors and eigenvalues of the system are approximated from a series of time-snapshots of the state variables. The…
We use direct statistical simulation (DSS) to find the low-order statistics of the well-known dynamical system, the Lorenz63 model. Instead of accumulating statistics from numerical simulation of the dynamical systems, we solve the…
Symbolic model checking of parallel programs stands and falls with effective methods of dealing with the explosion of interleavings. We propose a dynamic reduction technique to avoid unnecessary interleavings. By extending Lipton's original…
This technical note reviews sate-of-the-art algorithms for linear approximation of high-dimensional dynamical systems using low-rank dynamic mode decomposition (DMD). While repeating several parts of our article "low-rank dynamic mode…
This paper reports a development in the proper symplectic decomposition (PSD) for model reduction of forced Hamiltonian systems. As an analogy to the proper orthogonal decomposition (POD), PSD is designed to build a symplectic subspace to…
The dynamic mode decomposition (DMD) is a data-driven approach that extracts the dominant features from spatiotemporal data. In this work, we introduce sparse-mode DMD, a new variant of the optimized DMD framework that specifically…
Singular Value Decomposition (SVD) is a powerful tool in linear algebra.We propose an extension of SVD for both the qualitative detection and quantitative determination of nonlinearity in a time series. The paper illustrates nonlinear SVD…
High-fidelity large-eddy simulations are suitable to obtain insight into the complex flow dynamics in extended wind farms. In order to better understand these flow dynamics, we use dynamic mode decomposition (DMD) to analyze and reconstruct…
A common method to study deep learning systems is to use simplified model representations--for example, using singular value decomposition to visualize the model's hidden states in a lower dimensional space. This approach assumes that the…
This work establishes the equivalence of selected grid-forming control algorithms within the context of simplified theoretical models. Considered algorithms are droop control, Virtual Synchronous Machine (VSM) and matching control. It is…
The massive scale of pretrained models has made efficient compression essential for practical deployment. Low-rank decomposition based on the singular value decomposition (SVD) provides a principled approach for model reduction, but its…
Inspired by dynamic programming, we propose Stochastic Virtual Gradient Descent (SVGD) algorithm where the Virtual Gradient is defined by computational graph and automatic differentiation. The method is computationally efficient and has…
In this article, we consider the sparse tensor singular value decomposition, which aims for dimension reduction on high-dimensional high-order data with certain sparsity structure. A method named Sparse Tensor Alternating Thresholding for…