Related papers: Stochastic Algorithms for Self-consistent Calculat…
Conditional Random Fields (CRF) have been widely used in a variety of computer vision tasks. Conventional CRFs typically define edges on neighboring image pixels, resulting in a sparse graph such that efficient inference can be performed.…
Triboelectric charging of insulating particles through contact is critical in diverse physical and engineering processes, from dust storms and volcanic eruptions to industrial powder handling. However, many experiments over the years have…
With ever increasing data rates produced by modern radio telescopes like LOFAR and future telescopes like the SKA, many data processing steps are overwhelmed by the amount of data that needs to be handled using limited compute resources.…
In this paper, we propose and analyze a trust-region model-based algorithm for solving unconstrained stochastic optimization problems. Our framework utilizes random models of an objective function $f(x)$, obtained from stochastic…
A numerical method is proposed for a class of stochastic control problems including singular behavior. This method solves an infinite-dimensional linear program equivalent to the stochastic control problem using a finite element type…
Regular convergence, together with various other types of convergence, has been studied since the 1970s for the discrete approximations of linear operators. In this paper, we consider the eigenvalue approximation of compact operators whose…
Large sectors of the recent optimization literature focused in the last decade on the development of optimal stochastic first order schemes for constrained convex models under progressively relaxed assumptions. Stochastic proximal point is…
This paper presents a stochastic algorithm for iterative error control decoding. We show that the stochastic decoding algorithm is an approximation of the sum-product algorithm. When the code's factor graph is a tree, as with trellises, the…
The analysis of structure-preserving numerical methods for the Poisson--Nernst--Planck (PNP) system has attracted growing interests in recent years. In this work, we provide an optimal rate convergence analysis and error estimate for finite…
In this paper, we show that the Away-step Stochastic Frank-Wolfe Algorithm (ASFW) and Pairwise Stochastic Frank-Wolfe algorithm (PSFW) converge linearly in expectation. We also show that if an algorithm convergences linearly in expectation…
In this work, we mainly present the optimal convergence rates of the temporally second-order finite element scheme for solving the electrohydrodynamic equation. Suffering from the highly coupled nonlinearity, the convergence analysis of the…
We present an efficient and accurate method for calculating electronic structure and related properties of random alloys with a proper treatment of local environment effects. The method is a generalization of the locally self-consistent…
Coupled cluster methods are widely regarded as the gold standard of computational quantum chemistry as they are perceived to offer the best compromise between computational cost and a high-accuracy resolution of the ground state eigenvalue…
We present a mean-field approach to simulating merging processes of two spherical collisionless stellar systems. This approach is realized with a self-consistent field (SCF) method in which the full spatial dependence of the density and…
Recently we proposed an information entropy based method for electronic structure calculations within the density-matrix functional theory(DMFT) (Phys. Rev. Lett. 128, 013001), dubbed as $i$-DMFT. Comments have been raised regarding the…
Discretizing an analytic function on a uniform real-space grid is often done via a straightforward collocation method. This is ubiquitous in all areas of computational physics and quantum chemistry. An example in Density Functional Theory…
We propose and analyze novel adaptive algorithms for the numerical solution of elliptic partial differential equations with parametric uncertainty. Four different marking strategies are employed for refinement of stochastic Galerkin finite…
Motivated by applications in optimization and machine learning, we consider stochastic quasi-Newton (SQN) methods for solving stochastic optimization problems. In the literature, the convergence analysis of these algorithms relies on strong…
We present a stochastic variance-reduced heavy ball power iteration algorithm for solving PCA and provide a convergence analysis for it. The algorithm is an extension of heavy ball power iteration, incorporating a step size so that progress…
Exact approximations of Markov chain Monte Carlo (MCMC) algorithms are a general emerging class of sampling algorithms. One of the main ideas behind exact approximations consists of replacing intractable quantities required to run standard…