相关论文: Description of random level sets by polynomial cha…

This paper addresses the Bayesian calibration of dynamic models with parametric and structural uncertainties, in particular where the uncertain parameters are unknown/poorly known spatio-temporally varying subsystem models. Independent…

Due to significant manufacturing process variations, the performance of integrated circuits (ICs) has become increasingly uncertain. Such uncertainties must be carefully quantified with efficient stochastic circuit simulators. This paper…

Stochastic Galerkin methods offer unexplored potential for the numerical simulation of parabolic problems with random variables, in particular if they are combined with variational discretizations of the space and time variables. Due to the…

In this paper we study the numerical method for approximating the random periodic solution of semiliear stochastic evolution equations. The main challenge lies in proving a convergence over an infinite time horizon while simulating…

We present a new approach to using neural networks to approximate the solutions of variational equations, based on the adaptive construction of a sequence of finite-dimensional subspaces whose basis functions are realizations of a sequence…

The stochastic finite volume method offers an efficient one-pass approach for assessing uncertainty in hyperbolic conservation laws. Still, it struggles with the curse of dimensionality when dealing with multiple stochastic variables. We…

Polynomial chaos expansion is a popular way to develop surrogate models for stochastic systems with arbitrary random variables. Standard techniques such as Galerkin projection, stochastic collocation, and least squares approximation, are…

We develop efficient hierarchical preconditioners for optimal control problems governed by partial differential equations with uncertain coefficients. Adopting a discretize-then-optimize framework that integrates finite element…

This paper is a continuation of the work presented in [Chertock et al., Math. Cli. Weather Forecast. 5, 1 (2019), 65--106]. We study uncertainty propagation in warm cloud dynamics of weakly compressible fluids. The mathematical model is…

Near-optimal computational complexity of an adaptive stochastic Galerkin method with independently refined spatial meshes for elliptic partial differential equations is shown. The method takes advantage of multilevel structure in expansions…

The paper deals with a stochastic Galerkin approximation of elliptic Dirichlet boundary control problems with random input data. The expectation of a tracking cost functional with the deterministic constrained control is minimized. Error…

We consider kinetic vehicular traffic flow models of BGK type. Considering different spatial and temporal scales, those models allow to derive a hierarchy of traffic models including a hydrodynamic description. In this paper, the kinetic…

We develop generalized polynomial chaos (gPC) based stochastic Galerkin (SG) methods for a class of highly oscillatory transport equations that arise in semiclassical modeling of non-adiabatic quantum dynamics. These models contain…

The development of surrogate models to study uncertainties in hydrologic systems requires significant effort in the development of sampling strategies and forward model simulations. Furthermore, in applications where prediction time is…

In this work we focus on the construction of numerical schemes for the approximation of stochastic mean--field equations which preserve the nonnegativity of the solution. The method here developed makes use of a mean-field Monte Carlo…

A probabilistic approach of computing geometric rate of convergence of stochastic processes is introduced in this paper. The goal is to quantitatively compute both upper and lower bounds of the exponential rate of convergence to the…

A discontinuous Galerkin pressure correction numerical method for solving the incompressible Navier-Stokes equations is formulated and analyzed. We prove unconditional stability of the propose scheme. Convergence of the discrete velocity is…

Stochastic physical problems governed by nonlinear conservation laws are challenging due to solution discontinuities in stochastic and physical space. In this paper, we present a level set method to track discontinuities in stochastic space…

We present a new enriched Galerkin (EG) scheme for the Stokes equations based on piecewise linear elements for the velocity unknowns and piecewise constant elements for the pressure. The proposed EG method augments the conforming piecewise…

We investigate a numerical behaviour of robust deterministic optimal control problem subject to a convection diffusion equation containing uncertain inputs. Stochastic Galerkin approach, turning the original optimization problem containing…