相关论文: Regularized Reduced Order Models for a Stochastic …

We introduce a variational multiscale closure modeling strategy for the numerical stabilization of proper orthogonal decomposition reduced-order models of convection-dominated equations. As a first step, the new model is analyzed and tested…

Stochastic reduced-order models are widely used to represent the effective dynamics of complex systems, but estimating their drift and diffusion coefficients from data remains challenging. Standard approaches often rely on short-time…

This paper investigates the robust stability and stabilization analysis of interval fractional-order systems with time-varying delay. The stability problem of such systems is solved first, and then using the proposed results a stabilization…

In this paper, we propose a nonintrusive filter-based stabilization of reduced order models (ROMs) for uncertainty quantification (UQ) of the time-dependent Navier-Stokes equations in convection-dominated regimes. We propose a novel…

We present a statistical learning framework for robust identification of partial differential equations from noisy spatiotemporal data. Extending previous sparse regression approaches for inferring PDE models from simulated data, we address…

We present a stabilized POD-Galerkin reduced order method (ROM) for a Leray model. For the implementation of the model, we combine a two-step algorithm called Evolve-Filter (EF) with a computationally efficient finite volume method. In both…

Global stabilization of viscous Burgers' equation around constant steady state solution has been discussed in the literature. The main objective of this paper is to show global stabilization results for the 2D forced viscous Burgers'…

A nonintrusive model order reduction method for bilinear stochastic differential equations with additive noise is proposed. A reduced order model (ROM) is designed in order to approximate the statistical properties of high-dimensional…

Numerical stabilization is often used to eliminate (alleviate) the spurious oscillations generally produced by full order models (FOMs) in under-resolved or marginally-resolved simulations of convection-dominated flows. In this paper we…

Coherent structures are solutions to reaction-diffusion systems that are time-periodic in an appropriate moving frame and spatially asymptotic at $x=\pm\infty$ to spatially periodic travelling waves. This paper is concerned with sources…

A new approach to model order reduction of the Navier-Stokes equations at high Reynolds number is proposed. Unlike traditional approaches, this method does not rely on empirical turbulence modeling or modification of the Navier-Stokes…

Robust stability and stochastic stability have separately seen intense study in control theory for many decades. In this work we establish relations between these properties for discrete-time systems and employ them for robust control…

In this article we investigate the spatial Sobolev regularity of mild solutions to stochastic Burgers equations with additive trace class noise. Our findings are based on a combination of suitable bootstrap-type arguments and a detailed…

The paper is concerned with spatial and time regularity of solutions to linear stochastic evolution equation perturbed by L\'evy white noise "obtained by subordination of a Gaussian white noise". Sufficient conditions for spatial continuity…

Standard stochastic optimization methods are brittle, sensitive to stepsize choices and other algorithmic parameters, and they exhibit instability outside of well-behaved families of objectives. To address these challenges, we investigate…

In this paper, we study the strong and weak convergence rates for multi-scale one-dimensional stochastic Burgers equation. Based on the techniques of Galerkin approximation, Kolmogorov equation and Poisson equation, we obtain the slow…

We examine nonlinear dynamical systems of ordinary differential equations or differential algebraic equations. In an uncertainty quantification, physical parameters are replaced by random variables. The inner variables as well as a quantity…

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 article is devoted to the study of the existence and uniqueness of mild solution to time- and space-fractional stochastic Burgers equation perturbed by multiplicative white noise. The required results are obtained by stochastic…

Learning a stable Linear Dynamical System (LDS) from data involves creating models that both minimize reconstruction error and enforce stability of the learned representation. We propose a novel algorithm for learning stable LDSs. Using a…