Related papers: The tensor hypercontracted parametric reduced dens…
We present the working equations for a reduced-scaling method of evaluating the perturbative triples (T) energy in coupled-cluster theory, through the tensor hypercontraction (THC) of the triples amplitudes ($t_{ijk}^{abc}$). Through our…
Recently, Hohenstein et al[1] introduced tensor hypercontraction density fitting to decompose the rank-4 electron repulsion integral tensor as the product of five rank-2 tensors. In this paper, we use this methodology to construct an…
One method of representing a high-rank tensor as a (hyper-)product of lower-rank tensors is the tensor hypercontraction (THC) method of Hohenstein et al. This strategy has been found to be useful for reducing the polynomial scaling of…
We investigate a novel approach to approximate tensor-network contraction via the exact, matrix-free decomposition of full tensor-networks. We study this method as a means to eliminate the propagation of error in the approximation of…
We develop a quartic-scaling implementation of coupled-cluster singles and doubles based on low-rank tensor hypercontraction (THC) factorizations of both the electron repulsion integrals (ERIs) and the doubles amplitudes. This extends our…
Tensor network contractions are widely used in statistical physics, quantum computing, and computer science. We introduce a method to efficiently approximate tensor network contractions using low-rank approximations, where each intermediate…
We derive and implement a new way of solving coupled cluster equations with lower computational scaling. Our method is based on decomposition of both amplitudes and two electron integrals, using a combination of tensor hypercontraction and…
Electron repulsion integral tensor has ubiquitous applications in quantum chemistry calculations. In this work, we propose an algorithm which compresses the electron repulsion tensor into the tensor hypercontraction format with…
Tensor hypercontraction provides an attractive four-center two-electron repulsion integral format that can lower the scaling of many electronic structure methods while only requiring O(N^2) memory. However, in its grid-based least-squares…
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…
We report a complete implementation of the coupled-cluster method with single, double, and triple excitations (CCSDT) where tensor decompositions are used to reduce its scaling and overall computational costs. For the decomposition of the…
With the widespread use of self-consistent field methods, including Hartree-Fock and Density Functional Theory, the implications of accelerating these methods are immense. To this end, we develop a tensor hypercontraction construction with…
Tensor decomposition is a mathematically supported technique for data compression. It consists of applying some kind of a Low Rank Decomposition technique on the tensors or matrices in order to reduce the redundancy of the data. However, it…
In this paper, we propose a novel model to recover a low-rank tensor by simultaneously performing double nuclear norm regularized low-rank matrix factorizations to the all-mode matricizations of the underlying tensor. An block successive…
We consider the problem of recovering a low-multilinear-rank tensor from a small amount of linear measurements. We show that the Riemannian gradient algorithm initialized by one step of iterative hard thresholding can reconstruct an…
This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…
We present a low-scaling algorithm for the random phase approximation (RPA) with \textbf{k}-point sampling in the framework of tensor hypercontraction (THC) for electron repulsion integrals (ERIs). The THC factorization is obtained via a…
The problem of low-tubal-rank tensor estimation is a fundamental task with wide applications across high-dimensional signal processing, machine learning, and image science. Traditional approaches tackle such a problem by performing tensor…
This paper presents a multilevel tensor compression algorithm called tensor butterfly algorithm for efficiently representing large-scale and high-dimensional oscillatory integral operators, including Green's functions for wave equations and…
Two-body reduced density matrices (2RDMs) encode the essential two-electron physics of electronic states, but their quartic storage cost poses a major limitation in practical workflows. We investigate a simple protocol to compress both…