相关论文: Non-intrusive polynomial chaos expansion for topol…

This paper introduces an efficient sparse recovery approach for Polynomial Chaos (PC) expansions, which promotes the sparsity by breaking the dimensionality of the problem. The proposed algorithm incrementally explores sub-dimensional…

We develop a method to approximate the moments of a discrete-time stochastic polynomial system. Our method is built upon Carleman linearization with truncation. Specifically, we take a stochastic polynomial system with finitely many states…

In recent years, a growing number of cryptosystems based on chaos have been proposed. But most of them encountered many problems such as small key space and weak security. In the present paper, a new kind of chaotic cryptosystem based on…

This paper presents a distributed continuous-time optimization framework aimed at overcoming the challenges posed by time-varying cost functions and constraints in multi-agent systems, particularly those subject to disturbances. By…

We study second-order Consensus-Based Optimization (CBO), a derivative-free global optimization algorithm in which the consensus force and the multiplicative exploratory noise act on particle velocities. We prove quantitative…

In this paper we present an asymptotically compatible meshfree method for solving nonlocal equations with random coefficients, describing diffusion in heterogeneous media. In particular, the random diffusivity coefficient is described by a…

Verification solutions for uncertainty quantification are presented for time dependent transport problems where $c$, the scattering ratio, is uncertain. The method of polynomial chaos expansions is employed for quick and accurate…

A numerically efficient inverse method for parametric model uncertainty identification using maximum likelihood estimation is presented. The goal is to identify a probability model for a fixed number of model parameters based on a set of…

Stochastic compositional optimization arises in many important machine learning tasks such as value function evaluation in reinforcement learning and portfolio management. The objective function is the composition of two expectations of…

This article considers stochastic algorithms for efficiently solving a class of large scale non-linear least squares (NLS) problems which frequently arise in applications. We propose eight variants of a practical randomized algorithm where…

This paper studies the distributed optimization problem with possibly nonidentical local constraints, where its global objective function is composed of $N$ convex functions. The aim is to solve the considered optimization problem in a…

We consider stochastic optimization problems involving an expected value of a nonlinear function of a base random vector and a conditional expectation of another function depending on the base random vector, a dependent random vector, and…

Multi-physics models governed by coupled partial differential equation (PDE) systems, are naturally suited for partitioned, or modular numerical solution strategies. Although widely used in tackling deterministic coupled models, several…

We study random eigenvalue problems in the context of spectral stochastic finite elements. In particular, given a parameter-dependent, symmetric positive-definite matrix operator, we explore the performance of algorithms for computing its…

The paper builds upon a recent approach to find the approximate bounds of a real function using Polynomial Chaos expansions. Given a function of random variables with compact support probability distributions, the intuition is to quantify…

Identifying ordered structures hidden in the packings of particles is a common scientific question in multiple fields. In this work, we investigate the dynamical organizations of a large number of initially randomly packed repulsive…

We propose a novel polyhedral uncertainty set for robust optimization, termed the smooth uncertainty set, which captures dependencies of uncertain parameters by constraining their pairwise differences. The bounds on these differences may be…

Designing high-performance electric machines that maintain their efficiency and reliability under uncertain material and operating conditions is crucial for industrial applications. In this paper, we present a novel framework for robust…

The design of specified nonlinear mechanical responses into a structure or material is a highly sought after capability, which would have a significant impact in areas such as wave tailoring in metamaterials, impact mitigation, soft…

This chapter investigates how symmetries can be used to reduce the computational complexity in polynomial optimization problems. A focus will be specifically given on the Moment-SOS hierarchy in polynomial optimization, where results from…