Related papers: An additive two-level parallel variant of the DMRG…
The Density Matrix Renormalization Group (DMRG) algorithm has been a rising star for the accurate ab initio exploration of Born-Oppenheimer potential energy surfaces in theoretical chemistry. However, owing to its iterative numerical…
A biorthonormal-block density-matrix renormalization group algorithm is proposed to accurately compute properties of large-scale non-Hermitian many-body systems, in which a renormalized-space partition of the non-Hermitian reduced density…
Higher-order low-rank tensors naturally arise in many applications including hyperspectral data recovery, video inpainting, seismic data recon- struction, and so on. We propose a new model to recover a low-rank tensor by simultaneously…
The efficient solution of sparse, linear systems resulting from the discretization of partial differential equations is crucial to the performance of many physics-based simulations. The algorithmic optimality of multilevel approaches for…
Parallel-in-time methods for partial differential equations (PDEs) have been the subject of intense development over recent decades, particularly for diffusion-dominated problems. It has been widely reported in the literature, however, that…
We develop a multi-dimensional, parallelized domain decomposition strategy (DDC) for mass-transfer particle tracking (MTPT) methods. These methods are a type of Lagrangian algorithm for simulating reactive transport and are able to be…
We propose to boost the performance of the density matrix renormalization group (DMRG) in two dimensions by using Gutzwiller projected states as the initialization ansatz. When the Gutzwiller projected state is properly chosen, the…
The density matrix renormalization group (DMRG) is a powerful method to treat static correlation. Here we present an inexpensive way to add additional dynamic correlation energy to a DMRG self-consistent field (DMRG) wave function using…
In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model…
We propose a new tensor renormalization group algorithm, Anisotropic Tensor Renormalization Group (ATRG), for lattice models in arbitrary dimensions. The proposed method shares the same versatility with the Higher-Order Tensor…
We implement and apply time-dependent density matrix renormalization group (TD-DMRG) algorithms at zero and finite temperature to compute the linear absorption and fluorescence spectra of molecular aggregates. Our implementation is within a…
The main focus of this work is a novel framework for the joint reconstruction and segmentation of parallel MRI (PMRI) brain data. We introduce an image domain deep network for calibrationless recovery of undersampled PMRI data. The proposed…
Highly heterogeneous, anisotropic coefficients, e.g. in the simulation of carbon-fibre composite components, can lead to extremely challenging finite element systems. Direct solvers for the resulting large and sparse linear systems suffer…
Stochastic gradient descent (SGD) is a widely adopted iterative method for optimizing differentiable objective functions. In this paper, we propose and discuss a novel approach to scale up SGD in applications involving non-convex functions…
Current descriptions of the ab initio DMRG algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix…
We propose a novel many-body framework combining the density matrix renormalization group (DMRG) with the valence-space (VS) formulation of the in-medium similarity renormalization group. This hybrid scheme admits for favorable…
In this paper, we present GASG21 (Grassmannian Adaptive Stochastic Gradient for $L_{2,1}$ norm minimization), an adaptive stochastic gradient algorithm to robustly recover the low-rank subspace from a large matrix. In the presence of column…
We present the Copupled Cluster (CC) method and the Density matrix Renormalization Grooup (DMRG) method in a unified way, from the perspective of recent developments in tensor product approximation. We present an introduction into recently…
This work develops a novel set of algorithms, alternating Gradient Descent (GD) and minimization for MRI (altGDmin-MRI1 and altGDmin-MRI2), for accelerated dynamic MRI by assuming an approximate low-rank (LR) model on the matrix formed by…
We present a new implementation of the driven similarity renormalization group (DSRG) based on a density matrix renormalization group (DMRG) reference. The explicit build of high-order reduced density matrices is avoided by forming…