Related papers: Extended tensor decomposition model reduction meth…
Dynamic mode decomposition (DMD) is a data-driven method for estimating the dynamics of a discrete dynamical system. This paper proposes a tensor-based approach to DMD for applications in which the states can be viewed as tensors.…
In this paper, we focus on the fixed TT-rank and precision problems of finding an approximation of the tensor train (TT) decomposition of a tensor. Note that the TT-SVD and TT-cross are two well-known algorithms for these two problems.…
We introduce a new adaptive decomposition tool, which we refer to as Nonlinear Mode Decomposition (NMD). It decomposes a given signal into a set of physically meaningful oscillations for any waveform, simultaneously removing the noise. NMD…
Vertex direction algorithms have been around for a few decades in the experimental design and mixture models literature. We briefly review this type of algorithm and describe a new member of the family: the support reduction algorithm. The…
This paper presents a nonconforming finite element approximation of the space of symmetric tensors with square integrable divergence, on tetrahedral meshes. Used for stress approximation together with the full space of piecewise linear…
Tensors in the form of multilinear arrays are ubiquitous in data science applications. Captured real-world data, including video, hyperspectral images, and discretized physical systems, naturally occur as tensors and often come with…
Control of nonlinear distributed parameter systems (DPS) under uncertainty is a meaningful task for many industrial processes. However, both intrinsic uncertainty and high dimensionality of DPS require intensive computations, while…
The widespread use of multisensor technology and the emergence of big data sets have brought the necessity to develop more versatile tools to represent higher-order data with multiple aspects and high dimensionality. Data in the form of…
The evaluation of robustness and reliability of realistic structures in the presence of uncertainty involves costly numerical simulations with a very high number of evaluations. This motivates model order reduction techniques like the…
DeepTensor is a computationally efficient framework for low-rank decomposition of matrices and tensors using deep generative networks. We decompose a tensor as the product of low-rank tensor factors (e.g., a matrix as the outer product of…
We develop both first and second order numerical optimization methods to solve non-smooth optimization problems featuring a shared sparsity penalty, constrained by differential equations with uncertainty. To alleviate the curse of…
The recently proposed fully-connected tensor network (FCTN) decomposition has demonstrated significant advantages in correlation characterization and transpositional invariance, and has achieved notable achievements in multi-dimensional…
We develop theory for nonlinear dimensionality reduction (NLDR). A number of NLDR methods have been developed, but there is limited understanding of how these methods work and the relationships between them. There is limited basis for using…
Nonparametric extension of tensor regression is proposed. Nonlinearity in a high-dimensional tensor space is broken into simple local functions by incorporating low-rank tensor decomposition. Compared to naive nonparametric approaches, our…
Dual-energy X-ray Computed Tomography (DECT) constitutes an advanced technology which enables automatic decomposition of materials in clinical images without manual segmentation using the dependency of the X-ray linear attenuation with…
We consider large linear and nonlinear fixed point problems, and solution with proximal algorithms. We show that there is a close connection between two seemingly different types of methods from distinct fields: 1) Proximal iterations for…
Large language models (LLMs) demonstrate outstanding performance in various tasks in machine learning and have thus become one of the most important workloads in today's computing landscape. However, deploying LLM inference poses challenges…
Recent research has focused on designing neural samplers that amortize the process of sampling from unnormalized densities. However, despite significant advancements, they still fall short of the state-of-the-art MCMC approach, Parallel…
Low Rank Decomposition (LRD) is a model compression technique applied to the weight tensors of deep learning models in order to reduce the number of trainable parameters and computational complexity. However, due to high number of new…
Recently, numerous tensor singular value decomposition (t-SVD)-based tensor recovery methods have shown promise in processing visual data, such as color images and videos. However, these methods often suffer from severe performance…