Related papers: Variance reduction using antithetic variables for …

In recent years, machine learning models, chiefly deep neural networks, have revealed suited to learn accurate energy-density functionals from data. However, problematic instabilities have been shown to occur in the search of ground-state…

In this paper, a new approach based on convex analysis is introduced to solve the $H_\infty$ problem for discrete-time nonlinear stochastic systems. A stochastic version of bounded real lemma is proved and the state feedback $H_\infty$…

A homogenization result for a family of oscillating integral energies is presented, where the fields under consideration are subjected to first order linear differential constraints depending on the space variable x. The work is based on…

Efficient analysis and simulation of multiscale stochastic systems of chemical kinetics is an ongoing area for research, and is the source of many theoretical and computational challenges. In this paper, we present a significant improvement…

We propose a new \textit{quadratic programming-based} method of approximating a nonstandard density using a multivariate Gaussian density. Such nonstandard densities usually arise while developing posterior samplers for unobserved…

This article deals with the numerical approximation of effective coefficients in stochastic homogenization of discrete linear elliptic equations. The originality of this work is the use of a well-known abstract spectral representation…

We introduce a time-implicit, finite-element based space-time discretization scheme for the backward stochastic heat equation, and for the forward-backward stochastic heat equation from stochastic optimal control, and prove strong rates of…

In this paper, we propose a stochastic method for solving equality constrained optimization problems that utilizes predictive variance reduction. Specifically, we develop a method based on the sequential quadratic programming paradigm that…

Real-world physical systems, like composite materials and porous media, exhibit complex heterogeneities and multiscale nature, posing significant computational challenges. Computational homogenization is useful for predicting macroscopic…

We propose to homogenize a periodic (along one direction) structure, first in order to verify the quasi-static prediction of its response to an acoustic wave arising from mixing theory, then to address the question of what becomes of this…

This paper investigates the convergence of density approximations for stochastic heat equation in both uniform convergence topology and total variation distance. The convergence order of the densities in uniform convergence topology is…

We address the problem of estimating steady-state quantities associated to systems of stochastic chemical kinetics. In most cases of interest these systems are analytically intractable, and one has to resort to computational methods to…

We consider a non-stationary variant of a sequential stochastic optimization problem, in which the underlying cost functions may change along the horizon. We propose a measure, termed variation budget, that controls the extent of said…

We consider the solution of a stochastic convex optimization problem $\mathbb{E}[f(x;\theta^*,\xi)]$ over a closed and convex set $X$ in a regime where $\theta^*$ is unavailable and $\xi$ is a suitably defined random variable. Instead,…

This paper has two main goals: (a) establish several statistical properties---consistency, asymptotic distributions, and convergence rates---of stationary solutions and values of a class of coupled nonconvex and nonsmoothempirical risk…

Optimization problems with an auxiliary latent variable structure in addition to the main model parameters occur frequently in computer vision and machine learning. The additional latent variables make the underlying optimization task…

We study unconstrained optimization problems with nonsmooth and convex objective function in the form of a mathematical expectation. The proposed method approximates the expected objective function with a sample average function using…

We introduce a new method for studying stochastic homogenization of elliptic equations in nondivergence form. The main application is an algebraic error estimate, asserting that deviations from the homogenized limit are at most proportional…

In this paper, we show that the concept of sigma-convergence associated to stochastic processes can tackle the homogenization of stochastic partial differential equations. In this regard, the homogenization problem for a stochastic…

We prove the applicability of the Weighted Energy-Dissipation (WED) variational principle [50] to nonlinear parabolic stochastic partial differential equations in abstract form. The WED principle consists in the minimization of a…