Related papers: A dynamic domain semi-Lagrangian method for stocha…
The numerical evaluation of statistics plays a crucial role in statistical physics and its applied fields. It is possible to evaluate the statistics for a stochastic differential equation with Gaussian white noise via the corresponding…
In this paper we study stochastic quasi-Newton methods for nonconvex stochastic optimization, where we assume that only stochastic information of the gradients of the objective function is available via a stochastic first-order oracle…
Stochastic dynamics on sparse graphs and disordered systems often lead to complex behaviors characterized by heterogeneity in time and spatial scales, slow relaxation, localization, and aging phenomena. The mathematical tools and…
We consider in this paper travelling wave solutions to stochastic partial differential equations and corresponding wave speed. As a particular example we consider the Nagumo equation with multiplicative noise which we mainly consider in the…
In this paper we genealize the fast semi-Lagrangian scheme developed in [J. Comput. Phys., Vol. 255, 2013, pp 680-698] to the case of high order reconstructions of the distribution function. The original first order accurate semi-Lagrangian…
This paper presents a mesoscopic traffic flow model that explicitly describes the spatio-temporal evolution of the probability distributions of vehicle trajectories. The dynamics are represented by a sequence of factor graphs, which enable…
The subject of this work is a new stochastic Galerkin method for second-order elliptic partial differential equations with random diffusion coefficients. It combines operator compression in the stochastic variables with tree-based spline…
The aim of this work is to investigate semi-Lagrangian approximation schemes on unstructured grids for viscous transport and conservative equations with measurable coefficients that satisfy a one-sided Lipschitz condition. To establish the…
A positivity-preserving conservative semi-Lagrangian transport model by multi-moment finite volume method has been developed on the cubed-sphere grid. In this paper, two kinds of moments, i.e. point values (PV moment) at cell boundaries and…
This paper aims to investigate the numerical approximation of a general second order parabolic stochastic partial differential equation(SPDE) driven by multiplicative and additive noise. Our main interest is on such SPDEs where the…
We present approaches for the study of fluid-structure interactions subject to thermal fluctuations. A mixed mechanical description is utilized combining Eulerian and Lagrangian reference frames. We establish general conditions for…
In this paper, we present a new class of conservative semi-Lagrangian schemes for kinetic equations. They are based on the conservative reconstruction technique introduced in [S. Y. Cho, et al., Conservative semi-Lagrangian schemes for…
Semilinear, $N-$dimensional stochastic differential equations (SDEs) driven by additive L\'evy noise are investigated. Specifically, given $\alpha\in\left(\frac{1}{2},1\right)$, the interest is on SDEs driven by $2\alpha-$stable,…
Kinetic equations are difficult to solve numerically due to their high dimensionality. A promising approach for reducing computational cost is the dynamical low-rank algorithm, which decouples the dimensions of the phase space by proposing…
This paper proposes a multi-scale method to design a continuous-time distributed algorithm for constrained convex optimization problems by using multi-agents with Markov switched network dynamics and noisy inter-agent communications. Unlike…
This paper proposes a novel way to solve transient linear, and non-linear solid dynamics for compressible, nearly incompressible, and incompressible material in the updated Lagrangian framework for tetrahedral unstructured finite elements.…
This paper presents a general approach to linear stochastic processes driven by various random noises. Mathematically, such processes are described by linear stochastic differential equations of arbitrary order (the simplest non-trivial…
Motivated by distributed statistical learning over uncertain communication networks, we study distributed stochastic optimization by networked nodes to cooperatively minimize a sum of convex cost functions. The network is modeled by a…
In this work (Part I), we study three time-discretization procedures of the Dynamical Low-Rank Approximation (DLRA) of high-dimensional stochastic differential equations (SDEs). Specifically, we consider the Dynamically Orthogonal (DO)…
This paper develops and analyses semi-discrete numerical method for two dimensional Vlasov-Stokes' system with periodic boundary condition. The method is based on coupling of semi-discrete discontinuous Galerkin method for the Vlasov…