Article
Chemistry, Physical
Karl Pierce, Edward F. Valeev
Summary: This paper addresses the problem of constructing a canonical polyadic (CP) decomposition for a tensor network rather than a single tensor. It demonstrates how leveraging the structure of the network during CP factor optimization can reduce the complexity of constructing an approximate CP representation. The utility of this technique is shown for approximating the order-4 Coulomb interaction tensor with two order-3 tensors using an approximate generalized square-root (SQ) factorization.
JOURNAL OF CHEMICAL THEORY AND COMPUTATION
(2023)
Article
Computer Science, Artificial Intelligence
Mateusz Gabor, Rafal Zdunek
Summary: This study proposes a novel CNN compression technique based on the hierarchical Tucker-2 tensor decomposition, which achieves a significant reduction in parameters and FLOPS with a minor drop in classification accuracy. Compared to other compression methods, the HT-2 outperforms most of them.
APPLIED SOFT COMPUTING
(2023)
Article
Computer Science, Hardware & Architecture
Jun-Gi Jang, Moonjeong Park, Jongwuk Lee, Lee Sael
Summary: This article introduces a large-scale Tucker factorization method called the Very Sparse Tucker factorization (VeST) method for sparse and accurate tensor decomposition. The proposed VeST method outputs highly sparse decomposition results by iteratively determining unimportant elements and updating the remaining elements. Experiments demonstrate that VeST outperforms competitors in terms of accuracy and scalability.
JOURNAL OF SUPERCOMPUTING
(2022)
Article
Mathematics, Applied
Junjun Pan, Michael K. Ng, Ye Liu, Xiongjun Zhang, Hong Yan
Summary: This paper introduces an orthogonal nonnegative Tucker decomposition (ONTD) for nonnegative tensor data and develops a convex relaxation algorithm for solving the optimization problem of ONTD. The convergence of the algorithm is proved. ONTD is applied to image data sets from real-world applications, showing the effectiveness of the proposed algorithm through numerical results.
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2021)
Article
Chemistry, Physical
Peter Wind, Magnar Bjorgve, Anders Brakestad, Stig Rund Jensen, Roberto Di Remigio Eikas, Luca Frediani
Summary: MRChem is a code for molecular electronic structure calculations, featuring an adaptive basis representation and improved scalability. It can compete with traditional Gaussian-type orbital-based software in terms of performance.
JOURNAL OF CHEMICAL THEORY AND COMPUTATION
(2023)
Review
Engineering, Electrical & Electronic
Xingyi Liu, Keshab K. Parhi
Summary: This article discusses the importance of neural networks in complex CV and NLP tasks, and explores the effectiveness and benefits of using low-rank tensor approximations to compress model parameters.
IEEE CIRCUITS AND SYSTEMS MAGAZINE
(2023)
Article
Computer Science, Artificial Intelligence
Krzysztof Fonal, Rafal Zdunek
Summary: Tensor decomposition is a valuable method for multilinear feature extraction and dimensionality reduction of multiway data. In this study, a hierarchical Tucker decomposition model with single-mode preservation is proposed, along with various tensor augmentation strategies for image classification using multimodal tensor subspace analysis. Experiment results show that the proposed method outperforms well-known tensor decomposition algorithms.
Article
Computer Science, Information Systems
Yichun Qiu, Guoxu Zhou, Yu Zhang, Andrzej Cichocki
Summary: This study aims to enhance the scalability of tensor decompositions for big data analysis by proposing two algorithms that can handle huge dense tensors, with empirical evidence from extensive simulations demonstrating the validity and efficiency of the proposed algorithms.
MULTIMEDIA TOOLS AND APPLICATIONS
(2021)
Article
Engineering, Electrical & Electronic
Maxence Giraud, Vincent Itier, Remy Boyer, Yassine Zniyed, Andre L. F. de Almeida
Summary: Many signal-based applications utilize the Tucker decomposition of high-dimensional/order tensors. However, the curse of dimensionality, resulting in exponentially increasing entries, poses a challenge to the Tucker model. The Higher-Order Orthogonal Iteration (HOOI) and Higher-Order Singular Value Decomposition (HOSVD) are widely used but suffer from the same curse. In this letter, a new methodology called TRIDENT is proposed, which offers similar estimation accuracy as HOSVD but with significantly reduced computational and storage costs.
IEEE SIGNAL PROCESSING LETTERS
(2023)
Article
Computer Science, Information Systems
Xiaotong Yu, Ziyan Luo
Summary: A new method based on Tucker decomposition for sparse tensor optimization is proposed for improving background subtraction in video surveillance. By constraining the sparsity of video foreground and optimizing the low-rank characteristics of video background, the method enhances foreground detection accuracy and background estimation effectiveness.
MULTIMEDIA TOOLS AND APPLICATIONS
(2021)
Article
Computer Science, Artificial Intelligence
Zhihao Xu, Benjia Chu, Jianbo Li, Zhiqiang Lv
Summary: This study proposes a Fast Autoregressive Tensor Decomposition (FATD) algorithm for online real-time traffic flow prediction. The algorithm models and predicts historical traffic flow using Tucker decomposition and Tensor Seasonal Autoregressive Integrated Moving Average (Tensor SARIMA), and recovers the predicted traffic flow data using Inverse Tucker Decomposition, achieving reduced computational costs while maintaining high prediction accuracy.
KNOWLEDGE-BASED SYSTEMS
(2023)
Article
Mathematics, Applied
Linjian Ma, Edgar Solomonik
Summary: This paper introduces a novel family of algorithms that use perturbative corrections to optimize the quadratic optimization subproblems in CP and Tucker decomposition. The proposed pairwise perturbation algorithms are easy to control and achieve convergenceto minima that are as good as ALS.
NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS
(2022)
Article
Mathematics, Applied
Liqun Qi, Yannan Chen, Mayank Bakshi, Xinzhen Zhang
Summary: A new tensor decomposition method called triple decomposition is introduced in this paper, which decomposes a third order tensor into three factor tensors with low dimensions. Experimental results show that third order tensor data from practical applications have low triple ranks.
SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
(2021)
Article
Computer Science, Software Engineering
Zisen Fang, Fumin Qi, Yichuan Dong, Yong Zhang, Shengzhong Feng
Summary: This article focuses on parallel Tucker decomposition of dense tensors on distributed-memory systems. The proposed method utilizes hierarchical SVD to accelerate the SVD step and includes a data distribution strategy. It is found that the proposed method has lower communication cost compared to state-of-the-art methods in large-scale parallel cases.
CONCURRENCY AND COMPUTATION-PRACTICE & EXPERIENCE
(2023)
Article
Statistics & Probability
Bing-Yi Jing, Ting Li, Zhongyuan Lyu, Dong Xia
Summary: The study introduces a framework for community detection in multilayer networks, using a tensor-based algorithm to accurately reveal global/local memberships of nodes and layers. Numerical studies confirm the effectiveness of the method, which is applied to real datasets producing new and interesting findings.
ANNALS OF STATISTICS
(2021)
Article
Computer Science, Interdisciplinary Applications
Tian Liang, Lin Fu
Summary: In this work, a new shock-capturing framework is proposed based on a new candidate stencil arrangement and the combination of infinitely differentiable non-polynomial RBF-based reconstruction in smooth regions with jump-like non-polynomial interpolation for genuine discontinuities. The resulting scheme achieves high order accuracy and resolves genuine discontinuities with sub-cell resolution.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Lukas Lundgren, Murtazo Nazarov
Summary: In this paper, a high-order accurate finite element method for incompressible variable density flow is introduced. The method addresses the issues of saddle point system and stability problem through Schur complement preconditioning and artificial compressibility approaches, and it is validated to have high-order accuracy for smooth problems and accurately resolve discontinuities.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Gabriele Ciaramella, Laurence Halpern, Luca Mechelli
Summary: This paper presents a novel convergence analysis of the optimized Schwarz waveform relaxation method for solving optimal control problems governed by periodic parabolic PDEs. The analysis is based on a Fourier-type technique applied to a semidiscrete-in-time form of the optimality condition, which enables a precise characterization of the convergence factor at the semidiscrete level. The behavior of the optimal transmission condition parameter is also analyzed in detail as the time discretization approaches zero.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jonas A. Actor, Xiaozhe Hu, Andy Huang, Scott A. Roberts, Nathaniel Trask
Summary: This article introduces a scientific machine learning framework that uses a partition of unity architecture to model physics through control volume analysis. The framework can extract reduced models from full field data while preserving the physics. It is applicable to manifolds in arbitrary dimension and has been demonstrated effective in specific problems.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Nozomi Magome, Naoki Morita, Shigeki Kaneko, Naoto Mitsume
Summary: This paper proposes a novel strategy called B-spline based SFEM to fundamentally solve the problems of the conventional SFEM. It uses different basis functions and cubic B-spline basis functions with C-2-continuity to improve the accuracy of numerical integration and avoid matrix singularity. Numerical results show that the proposed method is superior to conventional methods in terms of accuracy and convergence.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Timothy R. Law, Philip T. Barton
Summary: This paper presents a practical cell-centred volume-of-fluid method for simulating compressible solid-fluid problems within a pure Eulerian setting. The method incorporates a mixed-cell update to maintain sharp interfaces, and can be easily extended to include other coupled physics. Various challenging test problems are used to validate the method, and its robustness and application in a multi-physics context are demonstrated.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Xing Ji, Fengxiang Zhao, Wei Shyy, Kun Xu
Summary: This paper presents the development of a third-order compact gas-kinetic scheme for compressible Euler and Navier-Stokes solutions, constructed particularly for an unstructured tetrahedral mesh. The scheme demonstrates robustness in high-speed flow computation and exhibits excellent adaptability to meshes with complex geometrical configurations.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Alsadig Ali, Abdullah Al-Mamun, Felipe Pereira, Arunasalam Rahunanthan
Summary: This paper presents a novel Bayesian statistical framework for the characterization of natural subsurface formations, and introduces the concept of multiscale sampling to localize the search in the stochastic space. The results show that the proposed framework performs well in solving inverse problems related to porous media flows.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jacob Rains, Yi Wang, Alec House, Andrew L. Kaminsky, Nathan A. Tison, Vamshi M. Korivi
Summary: This paper presents a novel method called constrained optimized DMD with Control (cOptDMDc), which extends the optimized DMD method to systems with exogenous inputs and can enforce the stability of the resulting reduced order model (ROM). The proposed method optimally places eigenvalues within the stable region, thus mitigating spurious eigenvalue issues. Comparative studies show that cOptDMDc achieves high accuracy and robustness.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Andrea La Spina, Jacob Fish
Summary: This work introduces a hybridizable discontinuous Galerkin formulation for simulating ideal plasmas. The proposed method couples the fluid and electromagnetic subproblems monolithically based on source and employs a fully implicit time integration scheme. The approach also utilizes a projection-based divergence correction method to enforce the Gauss laws in challenging scenarios. Numerical examples demonstrate the high-order accuracy, efficiency, and robustness of the proposed formulation.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Junhong Yue, Peijun Li
Summary: This paper proposes two numerical methods (IP-FEM and BP-FEM) to study the flexural wave scattering problem of an arbitrary-shaped cavity on an infinite thin plate. These methods successfully decompose the fourth-order plate wave equation into the Helmholtz and modified Helmholtz equations with coupled conditions on the cavity boundary, providing an effective solution to this challenging problem.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
William Anderson, Mohammad Farazmand
Summary: We develop fast and scalable methods, called RONS, for computing reduced-order nonlinear solutions. These methods have been proven to be highly effective in tackling challenging problems, but become computationally prohibitive as the number of parameters grows. To address this issue, three separate methods are proposed and their efficacy is demonstrated through examples. The application of RONS to neural networks is also discussed.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Marco Caliari, Fabio Cassini
Summary: In this paper, a second order exponential scheme for stiff evolutionary advection-diffusion-reaction equations is proposed. The scheme is based on a directional splitting approach and uses computation of small sized exponential-like functions and tensor-matrix products for efficient implementation. Numerical examples demonstrate the advantage of the proposed approach over state-of-the-art techniques.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Sebastiano Boscarino, Seung Yeon Cho, Giovanni Russo
Summary: This work proposes a high order conservative semi-Lagrangian method for the inhomogeneous Boltzmann equation of rarefied gas dynamics. The method combines a semi-Lagrangian scheme for the convection term, a fast spectral method for computation of the collision operator, and a high order conservative reconstruction and a weighted optimization technique to preserve conservative quantities. Numerical tests demonstrate the accuracy and efficiency of the proposed method.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)
Article
Computer Science, Interdisciplinary Applications
Jialei Li, Xiaodong Liu, Qingxiang Shi
Summary: This study shows that the number, centers, scattering strengths, inner and outer diameters of spherical shell-structured sources can be uniquely determined from the far field patterns. A numerical scheme is proposed for reconstructing the spherical shell-structured sources, which includes a migration series method for locating the centers and an iterative method for computing the inner and outer diameters without computing derivatives.
JOURNAL OF COMPUTATIONAL PHYSICS
(2024)