Related papers: Localized density matrix minimization and linear s…
We review the variational principle in the density matrix renormalization group (DMRG) method, which maximizes an approximate partition function within a restricted degrees of freedom; at zero temperature, DMRG mini- mizes the ground state…
In this paper, we focus on the local convergence rate analysis of the proximal iteratively reweighted $\ell_1$ algorithms for solving $\ell_p$ regularization problems, which are widely applied for inducing sparse solutions. We show that if…
Expectation-Maximization (EM) algorithm is a widely used iterative algorithm for computing (local) maximum likelihood estimate (MLE). It can be used in an extensive range of problems, including the clustering of data based on the Gaussian…
Predicting observables in equilibrium states is a central yet notoriously hard question in quantum many-body systems. In the physically relevant thermodynamic limit, certain mathematical formulations of this task have even been shown to…
We present a partition-free approach to the evolution of density matrices for open quantum systems coupled to a harmonic environment. The influence functional formalism combined with a two-time Hubbard-Stratonovich transformation allows us…
In this paper, we study numerical approximations of the ground states in finite temperature density functional theory. We formulate the problem with respect to the density matrices and justify the convergence of the finite dimensional…
We introduce a hybrid approach to applying the density matrix renormalization group (DMRG) to continuous systems, combining a grid approximation along one direction with a finite Gaussian basis set along the remaining two directions. This…
This paper considers an optimization problem for a dynamical system whose evolution depends on a collection of binary decision variables. We develop scalable approximation algorithms with provable suboptimality bounds to provide…
We present an algorithm based on maximum likelihood for the estimation and renormalization (marginalization) of exponential densities. The moment-matching problem resulting from the maximization of the likelihood is solved as an…
In this contribution, we are concerned with parameter optimization problems that are constrained by multiscale PDE state equations. As an efficient numerical solution approach for such problems, we introduce and analyze a new relaxed and…
The reduced-density-matrix method is an promising candidate for the next generation electronic structure calculation method; it is equivalent to solve the Schr\"odinger equation for the ground state. The number of variables is the same as a…
We develop a linearized boundary control method for the inverse boundary value problem of determining a density in the acoustic wave equation. The objective is to reconstruct an unknown perturbation in a known background density from the…
The low-complexity assumption in linear systems can often be expressed as rank deficiency in data matrices with generalized Hankel structure. This makes it possible to denoise the data by estimating the underlying structured low-rank…
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…
We derive a necessary and sufficient condition for the thermalization of a local observable in a closed quantum system which offers an alternative explanation, independent of the eigenstate thermalization hypothesis, for the thermalization…
In many applications of practical interest, solutions of partial differential equation models arise as critical points of an underlying (energy) functional. If such solutions are saddle points, rather than being maxima or minima, then the…
We study the problem of finding structured low-rank matrices using nuclear norm regularization where the structure is encoded by a linear map. In contrast to most known approaches for linearly structured rank minimization, we do not (a) use…
We introduce and compare new compression approaches to obtain regularized solutions of large linear systems which are commonly encountered in large scale inverse problems. We first describe how to approximate matrix vector operations with a…
The density matrix renormalization group (DMRG) algorithm was originally designed to efficiently compute the zero temperature or ground-state properties of one dimensional strongly correlated quantum systems. The development of the…
We are concerned with structured $\ell_0$-norms regularization problems, with a twice continuously differentiable loss function and a box constraint. This class of problems have a wide range of applications in statistics, machine learning…