7 citations · 16 across the 13 of their papers we have counts for
13 papers
Tensor-Train Methods for 3D Linear Elasticity: Block and Global Operator Representations with Solver Performance Analysis
Quoc Thai Tran, Duc P. Truong, William Dai +1
This work develops tensor-train (TT) formulations for solving large-scale three-dimensional linear elasticity problems discretized by isogeometric analysis. By exploiting the tenso…
A Tensor-Train Discontinuous Galerkin Method for the Vlasov-Maxwell System
Rujeko Chinomona, Dibyendu Adak, William J. Barham +4
We present a tensor-train discontinuous Galerkin (TT-DG) formulation for the Vlasov--Maxwell system that combines a modal DG discretization with low-rank tensor representations of…
Space-Time Spectral Collocation Tensor-Network Approach for Maxwell's Equations
Dibyendu Adak, Rujeko Chinomona, Duc P. Truong +3
In this work, we develop a space--time Chebyshev spectral collocation method for three-dimensional Maxwell's equations and combine it with tensor-network techniques in Tensor-Train…
A Tensor Train-Based Isogeometric Solver for Large-Scale 3D Poisson Problems on Complex Geometries
Quoc Thai Tran, Duc P. Truong, Kim Ø. Rasmussen +1
We introduce a three-dimensional (3D) fully tensor train (TT)-assembled isogeometric analysis (IGA) framework, TT-IGA, for solving partial differential equations (PDEs) on complex…
Breaking the Curse of Dimensionality: Solving Configurational Integrals for Crystalline Solids by Tensor Networks
Duc P. Truong, Benjamin Nebgen, Derek DeSantis +3
Accurately evaluating configurational integrals for dense solids remains a central and difficult challenge in the statistical mechanics of condensed systems. Here, we present a nov…
Space-Time Spectral Element Tensor Network Approach for Time Dependent Convection Diffusion Reaction Equation with Variable Coefficients
Dibyendu Adak, Duc P. Truong, Radoslav Vuchkov +5
In this paper, we present a new space-time Petrov-Galerkin-like method. This method utilizes a mixed formulation of Tensor Train (TT) and Quantized Tensor Train (QTT), designed for…
High-order Tensor-Train Finite Volume Method for Shallow Water Equations
Mustafa Engin Danis, Duc P. Truong, Derek DeSantis +3
In this paper, we introduce a high-order tensor-train (TT) finite volume method for the Shallow Water Equations (SWEs). We present the implementation of the order Upwind a…
Tensor Network Space-Time Spectral Collocation Method for Solving the Nonlinear Convection Diffusion Equation
Dibyendu Adak, M. Engin Danis, Duc P. Truong +2
Spectral methods provide highly accurate numerical solutions for partial differential equations, exhibiting exponential convergence with the number of spectral nodes. Traditionally…
Tensor Network Space-Time Spectral Collocation Method for Time Dependent Convection-Diffusion-Reaction Equations
Dibyendu Adak, Duc P. Truong, Gianmarco Manzini +2
Emerging tensor network techniques for solutions of Partial Differential Equations (PDEs), known for their ability to break the curse of dimensionality, deliver new mathematical me…
Tensor Networks for Solving Realistic Time-independent Boltzmann Neutron Transport Equation
Duc P. Truong, Mario I. Ortega, Ismael Boureima +3
Tensor network techniques, known for their low-rank approximation ability that breaks the curse of dimensionality, are emerging as a foundation of new mathematical methods for ultr…
Boolean Matrix Factorization via Nonnegative Auxiliary Optimization
Duc P. Truong, Erik Skau, Derek Desantis +1
A novel approach to Boolean matrix factorization (BMF) is presented. Instead of solving the BMF problem directly, this approach solves a nonnegative optimization problem with the c…
Factorization of Binary Matrices: Rank Relations, Uniqueness and Model Selection of Boolean Decomposition
Derek DeSantis, Erik Skau, Duc P. Truong +1
The application of binary matrices are numerous. Representing a matrix as a mixture of a small collection of latent vectors via low-rank decomposition is often seen as an advantage…
Determination of Latent Dimensionality in International Trade Flow
Duc P. Truong, Erik Skau, Vladimir I. Valtchinov +1
Currently, high-dimensional data is ubiquitous in data science, which necessitates the development of techniques to decompose and interpret such multidimensional (aka tensor) datas…