Related papers: Tensor-structured algorithm for reduced-order scal…

Density-functional theory (DFT) has revolutionized computer simulations in chemistry and material science. A faithful implementation of the theory requires self-consistent calculations. However, this effort involves repeatedly diagonalizing…

Density Functional Theory (DFT) is a pivotal method within quantum chemistry and materials science, with its core involving the construction and solution of the Kohn-Sham Hamiltonian. Despite its importance, the application of DFT is…

This paper proposes fast randomized algorithms for computing the Kronecker Tensor Decomposition (KTD). The proposed algorithms can decompose a given tensor into the KTD format much faster than the existing state-of-the-art algorithms. Our…

Tensors provide a structured representation for multidimensional data, yet discretization can obscure important information when such data originates from continuous processes. We address this limitation by introducing a functional Tucker…

We propose a strategy to compress and store large volumes of scientific data represented on unstructured grids. Approaches utilizing tensor decompositions for data compression have already been proposed. Here, data on a structured grid is…

We present an accurate and efficient framework for real-space Hubbard-corrected density functional theory. In particular, we obtain expressions for the energy, atomic forces, and stress tensor suitable for real-space finite-difference…

The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…

Kohn-Sham spin-density functional theory provides an efficient and accurate model to study electron-electron interaction effects in quantum dots, but its application to large systems is a challenge. An efficient algorithm for the…

Big data analysis has become a crucial part of new emerging technologies such as the internet of things, cyber-physical analysis, deep learning, anomaly detection, etc. Among many other techniques, dimensionality reduction plays a key role…

Tensor decompositions are promising tools for big data analytics as they bring multiple modes and aspects of data to a unified framework, which allows us to discover complex internal structures and correlations of data. Unfortunately most…

Locality of compact one-electron orbitals expanded strictly in terms of local subsets of basis functions can be exploited in density functional theory (DFT) to achieve linear growth of computation time with systems size, crucial in…

Given a set of Kohn-Sham orbitals from an insulating system, we present a simple, robust, efficient and highly parallelizable method to construct a set of, optionally orthogonal, localized basis functions for the associated subspace. Our…

Tensors of order three or higher have found applications in diverse fields, including image and signal processing, data mining, biomedical engineering and link analysis, to name a few. In many applications that involve for example time…

Quantum mechanical calculations for material modelling using Kohn-Sham density functional theory (DFT) involve the solution of a nonlinear eigenvalue problem for $N$ smallest eigenvector-eigenvalue pairs with $N$ proportional to the number…

We consider the problem of low-rank decomposition of incomplete multiway tensors. Since many real-world data lie on an intrinsically low dimensional subspace, tensor low-rank decomposition with missing entries has applications in many data…

Many applications in data science and scientific computing involve large-scale datasets that are expensive to store and compute with, but can be efficiently compressed and stored in an appropriate tensor format. In recent years, randomized…

Advanced algorithms for large-scale electronic structure calculations are mostly based on processing multi-dimensional sparse data. Examples are sparse matrix-matrix multiplications in linear-scaling Kohn-Sham calculations or the efficient…

Tensors are becoming increasingly common in data mining, and consequently, tensor factorizations are becoming more and more important tools for data miners. When the data is binary, it is natural to ask if we can factorize it into binary…

We develop new approximation algorithms and data structures for representing and computing with multivariate functions using the functional tensor-train (FT), a continuous extension of the tensor-train (TT) decomposition. The FT represents…

Linear-scaling techniques for Kohn-Sham density functional theory (KS-DFT) are essential to describe the ground state properties of extended systems. Still, these techniques often rely on the locality of the density matrix or on accurate…