Related papers: Localized density matrix minimization and linear s…
We investigate the numerical approximation of an elliptic optimal control problem which involves a nonconvex local regularization of the $L^q$-quasinorm penalization (with $q\in(0,1)$) in the cost function. Our approach is based on the…
We present and analyze a novel sparse polynomial technique for the simultaneous approximation of parameterized partial differential equations (PDEs) with deterministic and stochastic inputs. Our approach treats the numerical solution as a…
The large-scale focusing inversion of gravity and magnetic potential field data using $L_1$-norm regularization is considered. The use of the randomized singular value decomposition methodology facilitates tackling the computational…
Impressive progress has been made in the past decade in the study of technological applications of varied types of quantum systems. With industry giants like IBM laying down their roadmap for scalable quantum devices with more than…
We propose a method to obtain the thermal-equilibrium density matrix of a many-body quantum system using artificial neural networks. The variational function of the many-body density matrix is represented by a convolutional neural network…
We propose a marginal likelihood strategy within the Kennedy-O'Hagan (KOH) Bayesian framework, where a Gaussian process (GP) models the discrepancy between a physical system and its simulator. Our approach introduces a novel marginalized…
We investigate fully self-consistent multiscale quantum-classical algorithms on current generation superconducting quantum computers, in a unified approach to tackle the correlated electronic structure of large systems in both quantum…
We consider the problem of computing a positive definite $p \times p$ inverse covariance matrix aka precision matrix $\theta=(\theta_{ij})$ which optimizes a regularized Gaussian maximum likelihood problem, with the elastic-net regularizer…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…
This paper considers covariance matrix estimation of tensor data under high dimensionality. A multi-bandable covariance class is established to accommodate the need for complex covariance structures of multi-layer lattices and general…
We introduce a fresh scheme based on the local hidden variable models to quantify nonlocality for arbitrarily high-dimensional quantum systems. Our scheme explores the minimal amount of white noise that must be added to the system in order…
We develop computational methods for approximating the solution of a linear multi-term matrix equation in low rank. We follow an alternating minimization framework, where the solution is represented as a product of two matrices, and…
In this paper, we investigate the energy minimization model of the ensemble Kohn-Sham density functional theory for metallic systems, in which a pseudo-eigenvalue matrix and a general smearing approach are involved. We study the invariance…
A new method is presented which allows time averaged density matrices of closed quantum systems to be computed via a constraint overlap maximization. Due to its simplicity, this method can be combined with algorithms based on tensor…
We propose in this contribution a method for l one regularization in prototype based relevance learning vector quantization (LVQ) for sparse relevance profiles. Sparse relevance profiles in hyperspectral data analysis fade down those…
We introduce two new particle-based algorithms for learning latent variable models via marginal maximum likelihood estimation, including one which is entirely tuning-free. Our methods are based on the perspective of marginal maximum…
In this paper, we propose a low rank approximation method for efficiently solving stochastic partial differential equations. Specifically, our method utilizes a novel low rank approximation of the stiffness matrices, which can significantly…
We propose a systematic procedure for the approximation of density functionals in density functional theory that consists of two parts. First, for the efficient approximation of a general density functional, we introduce an efficient ansatz…
This paper is concerned with the numerical minimization of energy functionals in Hilbert spaces involving convex constraints coinciding with a semi-norm for a subspace. The optimization is realized by alternating minimizations of the…
In this work we investigate the relationship between Bregman distances and regularized Logistic Regression model. We present a detailed study of Bregman Distance minimization, a family of generalized entropy measures associated with convex…