Related papers: Open-shell Tensor Hypercontraction
We propose a multireference linearized coupled cluster theory using matrix product states (MPS-LCC) which provides remarkably accurate ground-state energies, at a computational cost that has the same scaling as multireference configuration…
The transcorrelated (TC) method performs a similarity transformation on the electronic Schr\"odinger equation via Jastrow factorization of the wave function. This has demonstrated significant advancements in computational electronic…
We present a cost-reduced approach for the distinguishable cluster approximation to coupled cluster with singles, doubles and iterative triples (DC-CCSDT) based on a tensor decomposition of the triples amplitudes. The triples amplitudes and…
The widespread use of multisensor technology and the emergence of big datasets have created the need to develop tools to reduce, approximate, and classify large and multimodal data such as higher-order tensors. While early approaches…
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…
Block tensor decomposition (BTD) and canonical polyadic decomposition (CPD) are combined into a unified $O(N^3)$-scaling framework for second-order perturbation theory (PT2), demonstrated on MP2 and renormalized PT2 (rPT2). BTD constructs…
Unitary Coupled Cluster (UCC) theory is a promising variational method for electronic structure calculations, especially for strongly correlated systems and quantum computers. However, its practical application is limited by the steep…
Tensor computations--in particular tensor contraction (TC)--are important kernels in many scientific computing applications. Due to the fundamental similarity of TC to matrix multiplication (MM) and to the availability of optimized…
In this paper, a least-squares finite element method for scalar nonlinear hyperbolic balance laws is proposed and studied. The approach is based on a formulation that utilizes an appropriate Helmholtz decomposition of the flux vector and is…
Motivated by the recent observations of $T^*_{cs0}(2870)^0$, $T^*_{c\bar s 0}(2900)^0$ and $T^*_{c\bar s 0}(2900)^{++}$ open-charmed tetraquark states by LHCb, we study the decays of heavy mesons to these open-charmed tetraquark states…
Within the tensor singular value decomposition (T-SVD) framework, existing robust low-rank tensor completion approaches have made great achievements in various areas of science and engineering. Nevertheless, these methods involve the T-SVD…
We introduce a tensor-based clustering method to extract sparse, low-dimensional structure from high-dimensional, multi-indexed datasets. This framework is designed to enable detection of clusters of data in the presence of structural…
As an essential attribute of organic compounds, polarity has a profound influence on many molecular properties such as solubility and phase transition temperature. Thin layer chromatography (TLC) represents a commonly used technique for…
The alternating least squares (ALS/AltLS) method is a widely used algorithm for computing the CP decomposition of a tensor. However, its convergence theory is still incompletely understood. In this paper, we prove explicit quantitative…
A series of third- and fifth-order hybrid compact least-squares central weighted essentially non-oscillatory schemes are proposed and applied to curvilinear structured grids for the finite volume method. In smooth regions, compact…
Compressed sensing (CS) exploits the sparsity of a signal in order to integrate acquisition and compression. CS theory enables exact reconstruction of a sparse signal from relatively few linear measurements via a suitable nonlinear…
A novel reduced-scaling, general-order coupled-cluster approach is formulated by exploiting hierarchical representations of many-body tensors, combined with the recently suggested formalism of scale-adaptive tensor algebra. Inspired by the…
We present efficient implementations of the multilevel CC2 (MLCC2) and multilevel CCSD (MLCCSD) models. As the system size increases, MLCC2 and MLCCSD exhibit the scaling of the lower level coupled cluster model. In order to treat large…
Alternating least squares is the most widely used algorithm for CP tensor decomposition. However, alternating least squares may exhibit slow or no convergence, especially when high accuracy is required. An alternative approach is to regard…
A method of cluster diagonalization in a systematically expanded Hilbert space is described. We discuss some applications of this procedure to models of high-T_c superconductors, like the t - J and one and three bands Hubbard models in two…