Related papers: Stochastic Algorithms for Self-consistent Calculat…
In this contribution, we present a full overview of the continuous stochastic gradient (CSG) method, including convergence results, step size rules and algorithmic insights. We consider optimization problems in which the objective function…
Constant potential molecular dynamics simulation plays important role for applications of electrochemical systems, yet the calculation of charge fluctuation on electrodes remains a computational bottleneck. We propose a highly scalable,…
We consider in this work a system of two stochastic differential equations named the perturbed compositional gradient flow. By introducing a separation of fast and slow scales of the two equations, we show that the limit of the slow motion…
We propose a self-consistent method for electronic structure calculations of correlated systems, which combines the local spin-density approximation (LSDA) and the dynamical mean field theory (DMFT). The LSDA part is based on the exact…
Classical stochastic gradient methods are well suited for minimizing expected-value objective functions. However, they do not apply to the minimization of a nonlinear function involving expected values or a composition of two expected-value…
Under mild assumptions stochastic gradient methods asymptotically achieve an optimal rate of convergence if the arithmetic mean of all iterates is returned as an approximate optimal solution. However, in the absence of stochastic noise, the…
In this paper, we propose stochastic structure-preserving schemes to compute the effective diffusivity for particles moving in random flows. We first introduce the motion of particles using the Lagrangian formulation, which is modeled by…
In network analysis, developing a unified theoretical framework that can compare methods under different models is an interesting problem. This paper proposes a partial solution to this problem. We summarize the idea of using separation…
The vast majority of convergence rates analysis for stochastic gradient methods in the literature focus on convergence in expectation, whereas trajectory-wise almost sure convergence is clearly important to ensure that any instantiation of…
The common spatial pattern analysis (CSP) is a widely used signal processing technique in brain-computer interface (BCI) systems to increase the signal-to-noise ratio in electroencephalogram (EEG) recordings. Despite its popularity, the…
We consider the minimization of composite objective functions composed of the expectation of quadratic functions and an arbitrary convex function. We study the stochastic dual averaging algorithm with a constant step-size, showing that it…
We study the computation of equilibrium points of electrostatic potentials: locations in space where the electrostatic force arising from a collection of charged particles vanishes. This is a novel scenario of optimization in which…
We present the method of the self-consistent calculation of thermodynamical and correlation functions. This approach is based on the GRPA (generalized random phase approximation) scheme with the inclusion of the mean field corrections.…
Consider a probability measure supported by a regular geodesic ball in a manifold. For any p larger than or equal to 1 we define a stochastic algorithm which converges almost surely to the p-mean of the measure. Assuming furthermore that…
We review our recently developed electronic structure calculation methods used for the dynamics of large-scale solids or liquids with an efficient algorithm for large scale simultaneous linear equations. The electronic structure calculation…
A self-consistent method for calculating electron transport through a molecular device is proposed. It is based on density functional theory electronic structure calculations under periodic boundary conditions and implemented in the…
The thin plate spline smoother is a classical model for fnding a smooth function from the knowledge of its observation at scattered locations which may have random noises. We consider a nonconforming Morley finite element method to…
We propose a unified framework to speed up the existing stochastic matrix factorization (SMF) algorithms via variance reduction. Our framework is general and it subsumes several well-known SMF formulations in the literature. We perform a…
Spectral clustering is one of the most popular methods for community detection in graphs. A key step in spectral clustering algorithms is the eigen decomposition of the $n{\times}n$ graph Laplacian matrix to extract its $k$ leading…
Large-scale applications of energy density functional (EDF) methods depend on fast and reliable algorithms to solve the associated non-linear self-consistency problem. When dealing with large single-particle variational spaces, existing…