Related papers: Gradient-based stochastic estimation of the densit…

Electronic density of states (DOS) is a key factor in condensed matter physics and material science that determines the properties of metals. First-principles density-functional theory (DFT) calculations have typically been used to obtain…

Determining the 3D structures of biological molecules is a key problem for both biology and medicine. Electron Cryomicroscopy (Cryo-EM) is a promising technique for structure estimation which relies heavily on computational methods to…

We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the…

Extracting scientific results from high-energy collider data involves the comparison of data collected from the experiments with synthetic data produced from computationally-intensive simulations. Comparisons of experimental data and…

We propose a distributed Quantum State Tomography (QST) protocol, named Local Stochastic Factored Gradient Descent (Local SFGD), to learn the low-rank factor of a density matrix over a set of local machines. QST is the canonical procedure…

Stochastic coordinate descent algorithms are efficient methods in which each iterate is obtained by fixing most coordinates at their values from the current iteration, and approximately minimizing the objective with respect to the remaining…

Gradient-based optimization methods are commonly used to identify local optima in high-dimensional spaces. When derivatives cannot be evaluated directly, stochastic estimators can provide approximate gradients. However, these estimators'…

Electronic structure calculation of atoms and molecules, in the past few decades has largely been dominated by density functional methods. This is primarily due to the fact that this can account for electron correlation effects in a…

Gradient methods are widely used in optimization problems. In practice, while the smoothness parameter can be estimated utilizing techniques such as backtracking, estimating the strong convexity parameter remains a challenge; moreover, even…

A design optimization framework for process parameters of additive manufacturing based on finite element simulation is proposed. The finite element method uses a coupled thermomechanical model developed for fused deposition modeling from…

We consider the energy-driven stochastic state vector reduction equation for the density matrix, which for pure state density matrices can be written in two equivalent forms. We use these forms to discuss the decoupling of the noise terms…

A number of optimization approaches have been proposed for optimizing nonconvex objectives (e.g. deep learning models), such as batch gradient descent, stochastic gradient descent and stochastic variance reduced gradient descent. Theory…

Estimating the temperature and metal abundance of the intracluster and the intragroup media is crucial to determine their global metal content and to determine fundamental cosmological parameters. When a spatially resolved temperature or…

Simulations in the warm dense matter regime using finite temperature Kohn-Sham density functional theory (FT-KS-DFT), while frequently used, are computationally expensive due to the partial occupation of a very large number of high-energy…

The density functional theory (DFT) in electronic structure calculations can be formulated as either a nonlinear eigenvalue or direct minimization problem. The most widely used approach for solving the former is the so-called…

In this work, the development and implementation of the effective stochastic potential (ESP) method is presented to perform efficient conformational sampling of molecules. The overarching goal of this work is to alleviate the computational…

The paper considers the problem of network-based computation of global minima in smooth nonconvex optimization problems. It is known that distributed gradient-descent-type algorithms can achieve convergence to the set of global minima by…

A theoretical analysis is given of the equation of motion method, due to Alben et al., to compute the eigenvalue distribution (density of states) of very large matrices. The salient feature of this method is that for matrices of the kind…

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 present a convergence rate analysis for biased stochastic gradient descent (SGD), where individual gradient updates are corrupted by computation errors. We develop stochastic quadratic constraints to formulate a small linear matrix…