Related papers: Model order reduction for stochastic dynamical sys…

In this paper we analyze a zeroth-order proximal stochastic gradient method suitable for the minimization of weakly convex stochastic optimization problems. We consider nonsmooth and nonlinear stochastic composite problems, for which…

Shape-constrained optimization arises in a wide range of problems including distributionally robust optimization (DRO) that has surging popularity in recent years. In the DRO literature, these problems are usually solved via reduction into…

We exhibit an alternative method for solving inhomogeneous second--order linear ordinary dynamic equations on time scales, based on reduction of order rather than variation of parameters. Our form extends recent (and long-standing) analysis…

The dynamic mode decomposition (DMD) has become a leading tool for data-driven modeling of dynamical systems, providing a regression framework for fitting linear dynamical models to time-series measurement data. We present a simple…

Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. Here, we explore the use of Neural Ordinary Differential Equations, a recently introduced family of…

This paper presents a novel model order reduction technique tailored for power systems with a large share of inverter-based energy resources. Such systems exhibit an increased level of dynamic stiffness compared to traditional power…

This paper develops and analyzes an optimal-order semi-discrete scheme and its fully discrete finite element approximation for nonlinear stochastic elastic wave equations with multiplicative noise. A non-standard time-stepping scheme is…

Recently, convex nested stochastic composite optimization (NSCO) has received considerable attention for its applications in reinforcement learning and risk-averse optimization. The current NSCO algorithms have worse stochastic oracle…

We propose a parallel algorithm for the numerical solution of a class of second order semi-linear equations coming from stochastic optimal control problems, by means of a dynamic domain decomposition technique. The new method is an…

We present the Super-Localized Orthogonal Decomposition (SLOD) method for the numerical homogenization of linear elasticity problems with multiscale microstructures modeled by a heterogeneous coefficient field without any periodicity or…

We propose a new reduced order modeling strategy for tackling parametrized Partial Differential Equations (PDEs) with linear constraints, in particular Darcy flow systems in which the constraint is given by mass conservation. Our approach…

Stochastic Gradient Descent (SGD) methods see many uses in optimization problems. Modifications to the algorithm, such as momentum-based SGD methods have been known to produce better results in certain cases. Much of this, however, is due…

This paper focuses on the construction and analysis of explicit numerical methods of high dimensional stochastic nonlinear Schrodinger equations (SNLSEs). We first prove that the classical explicit numerical methods are unstable and suffer…

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…

In this paper, we present a new stochastic algorithm, namely the stochastic block mirror descent (SBMD) method for solving large-scale nonsmooth and stochastic optimization problems. The basic idea of this algorithm is to incorporate the…

We present a method of exploiting symmetries of discrete-time optimal control problems to reduce the dimensionality of dynamic programming iterations. The results are derived for systems with continuous state variables, and can be applied…

Reduced order models play an important role in the design, optimization and control of dynamical systems. In recent years, there has been an increasing interest in the application of data-driven techniques for model reduction that can…

Stochastic compositional optimization (SCO) has attracted considerable attention because of its broad applicability to important real-world problems. However, existing works on SCO assume that the projection within a solution update is…

Distributionally robust optimization (DRO) problems are increasingly seen as a viable method to train machine learning models for improved model generalization. These min-max formulations, however, are more difficult to solve. We therefore…

This paper considers the distributed convex-concave minimax optimization under the second-order similarity. We propose stochastic variance-reduced optimistic gradient sliding (SVOGS) method, which takes the advantage of the finite-sum…