Related papers: A Simple Collocation-Type Approach to Numerical St…

The combination of reduced basis and collocation methods enables efficient and accurate evaluation of the solutions to parameterized PDEs. In this paper, we study the stochastic collocation methods that can be combined with reduced basis…

We address the numerical approximation of Mean Field Games with local couplings. For power-like Hamiltonians, we consider both unconstrained and constrained stationary systems with density constraints in order to model hard congestion…

This paper presents a new approach to statistical similarity assessment based on sequence alignment. The algorithm performs mutual matching of two random sequences by successively searching for common elements and by applying sequence…

Stochastic contact Hamiltonian systems are a class of important mathematical models, which can describe the dissipative properties with odd dimensions in the stochastic environment. In this article, we investigate the numerical dynamics of…

An original graph clustering approach to efficient localization of error covariances is proposed within an ensemble-variational data assimilation framework. Here the localization term is very generic and refers to the idea of breaking up a…

The two-scale computational homogenization method is proposed for modelling of locally periodic fluid-saturated media subjected a to large deformation induced by quasistatic loading. The periodic heterogeneities are relevant to the…

We present in this paper an approach for computing the homogenized behavior of a medium that is a small random perturbation of a periodic reference material. The random perturbation we consider is, in a sense made precise in our work, a…

We consider a stochastic heat equation with nonlinear finite-rank space-coloured multiplicative noise that admits a unique nonnegative solution when given nonnegative initial data. Inspired by existing results for fully discrete finite…

We develop and analyse numerical schemes for uncertainty quantification in neural field equations subject to random parametric data in the synaptic kernel, firing rate, external stimulus, and initial conditions. The schemes combine a…

In recent years, the paradigm of cloud computing has emerged as an architecture for computing that makes use of distributed (networked) computing resources. In this paper, we consider a distributed computing algorithmic scheme for…

We propose a multiscale method for mixed-dimensional elliptic problems with highly heterogeneous coefficients arising, for example, in the modeling of fractured porous media. The method is based on the Localized Orthogonal Decomposition…

Majorization-minimization schemes are a broad class of iterative methods targeting general optimization problems, including nonconvex, nonsmooth and stochastic. These algorithms minimize successively a sequence of upper bounds of the…

The sensor placement problem is a common problem that arises when monitoring correlated phenomena, such as temperature, precipitation, and salinity. Existing approaches to this problem typically formulate it as the maximization of…

We propose a new information aggregation method which called Localized Feature Aggregation Module based on the similarity between the feature maps of an encoder and a decoder. The proposed method recovers positional information by…

We consider a nonlinear convex stochastic homogenization problem, in a stationary setting. In practice, the deterministic homogenized energy density can only be approximated by a random apparent energy density, obtained by solving the…

In this paper, we develop a numerical multiscale method to solve the fractional Laplacian with a heterogeneous diffusion coefficient. When the coefficient is heterogeneous, this adds to the computational costs. Moreover, the fractional…

Motivated by a wide variety of applications, this paper introduces a general class of networks of stochastic loss systems in which congestion renders lost revenue due to customers or jobs being permanently removed from the system. We seek…

Theories of localised pattern formation are important to understand a broad range of natural patterns, but are less well-understood than more established mechanisms of domain-filling pattern formation. Here, we extend recent work on pattern…

Homogenization of a thin micro-structure yields effective jump conditions that incorporate the geometrical features of the scatterers. These jump conditions apply across a thin but nonzero thickness interface whose interior is disregarded.…

In this paper, we propose a multilevel stochastic framework for the solution of nonconvex unconstrained optimization problems. The proposed approach uses random regularized first-order models that exploit an available hierarchical…