Related papers: Tensor Product Approximation (DMRG) and Coupled Cl…
The Density Matrix Renormalization Group (DMRG) method scales exponentially in the system width for models in two dimensions, but remains one of the most powerful methods for studying 2D systems with a sign problem. Reviewing past…
The CP tensor decomposition is a low-rank approximation of a tensor. We present a distributed-memory parallel algorithm and implementation of an alternating optimization method for computing a CP decomposition of dense tensor data that can…
The Density Matrix Renormalization Group (DMRG) was introduced by Steven White in 1992 as a method for accurately describing the properties of one-dimensional quantum lattices. The method, as originally introduced, was based on the…
Tensor classification has become increasingly crucial in statistics and machine learning, with applications spanning neuroimaging, computer vision, and recommendation systems. However, the high dimensionality of tensors presents significant…
We propose a simple modification of the density matrix renormalization group (DMRG) method in order to tackle strongly disordered quantum spin chains. Our proposal, akin to the idea of the adaptive time-dependent DMRG, enables us to reach…
Point-mass filters solve Bayesian recursive relations by approximating probability density functions of a system state over grids of discrete points. The approach suffers from the curse of dimensionality. The exponential increase of the…
In this paper, we propose and analyze the numerical algorithms for fast solution of periodic elliptic problems in random media in $\mathbb{R}^d$, $d=2,3$. We consider the stochastic realizations using checkerboard configuration of the…
A major advance in density-matrix renormalization group (DMRG) calculations has been achieved by the invention of highly efficient DMRG techniques for the simulation of real-time dynamics of strongly correlated quantum systems in one…
Deep neural networks (DNNs) have enabled impressive breakthroughs in various artificial intelligence (AI) applications recently due to its capability of learning high-level features from big data. However, the current demand of DNNs for…
Channel pruning and tensor decomposition have received extensive attention in convolutional neural network compression. However, these two techniques are traditionally deployed in an isolated manner, leading to significant accuracy drop…
We present a unified framework for renormalization group methods, including Wilson's numerical renormalization group (NRG) and White's density-matrix renormalization group (DMRG), within the language of matrix product states. This allows…
In this paper, we introduce a method for multivariate function approximation using function evaluations, Chebyshev polynomials, and tensor-based compression techniques via the Tucker format. We develop novel randomized techniques to…
This paper investigates the approximation of functions with finite smoothness defined on domains with a Cartesian product structure. The recently proposed tensor product multilevel method (TPML) combines Smolyak's sparse grid method with a…
We have devised and implemented a local ab initio Density Matrix Renormalization Group (DMRG) algorithm to describe multireference nondynamic correlations in large systems. For long molecules that are extended in one of their spatial…
Attempts of studying implicit regularization associated to gradient descent (GD) have identified matrix completion as a suitable test-bed. Late findings suggest that this phenomenon cannot be phrased as a minimization-norm problem, implying…
The objective of this paper is to investigate a new numerical method for the approximation of the self-diffusion matrix of a tagged particle process defined on a grid. While standard numerical methods make use of long-time averages of…
We present a numerical implementation of the density matrix renormalization group (DMRG) using the discrete variable representation (DVR) basis set. One main advantage of using the local DVR basis sets is that the computations of…
Quantum state tomography is a key technique for quantum information processing, but is challenging due to the exponential growth of its complexity with the system size. In this work, we propose an algorithm which iteratively finds the best…
This paper is concerned with the approximation of tensors using tree-based tensor formats, which are tensor networks whose graphs are dimension partition trees. We consider Hilbert tensor spaces of multivariate functions defined on a…
This article compares the tensor method density matrix renormalization group (DMRG) with two neural network based methods -namely FermiNet and PauliNet) for determining the ground state wavefunction of the many-body electronic…