相关论文: Resolve subgrid microscale interactions to discret…

This paper provides a small noise approximation for local random center manifolds of a class of stochastic dynamical systems in Euclidean space. An example is presented to illustrate the method.

For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…

In this paper, we consider a new approach for semi-discretization in time and spatial discretization of a class of semi-linear stochastic partial differential equations (SPDEs) with multiplicative noise. The drift term of the SPDEs is only…

A large toolbox of numerical schemes for dispersive equations has been established, based on different discretization techniques such as discretizing the variation-of-constants formula (e.g., exponential integrators) or splitting the full…

Stochastic gradient descent (SGD) has been widely used in machine learning due to its computational efficiency and favorable generalization properties. Recently, it has been empirically demonstrated that the gradient noise in several deep…

The problem of structured noise suppression is addressed by i)modelling the subspaces hosting the components of the signal conveying the information and ii)applying a non-extensive nonlinear technique for effecting the right separation.…

We develop a formalism to describe the discrete-time dynamics of systems containing an arbitrary number of interacting species. The individual-based model, which forms our starting point, is described by a Markov chain, which in the limit…

In this paper, we study temporal splitting algorithms for multiscale problems. The exact fine-grid spatial problems typically require some reduction in degrees of freedom. Multiscale algorithms are designed to represent the fine-scale…

Starting from the simple point process model of 1/f noise we derive a stochastic nonlinear differential equation for the signal exhibiting 1/f noise in any desirably wide range of frequency. A stochastic differential equation (the general…

We analyse the nonlinear Kuramoto-Sivashinsky equation to develop an accurate finite difference approximation to its dynamics. The analysis is based upon centre manifold theory so we are assured that the finite difference model accurately…

It is known that the solution of a conservative steady-state two-sided fractional diffusion problem can exhibit singularities near the boundaries. As consequence of this, and due to the conservative nature of the problem, we adopt a finite…

Statistical (machine learning) tools for equation discovery require large amounts of data that are typically computer generated rather than experimentally observed. Multiscale modeling and stochastic simulations are two areas where learning…

We consider the numerical approximation of a general second order semi--linear parabolic stochastic partial differential equation (SPDEs) driven by space-time noise, for multiplicative and additive noise. We examine convergence of…

This paper is devoted to proving the small noise asymptotic behaviour, particularly large deviation principle, for multi-scale stochastic dynamical systems with fully local monotone coefficients driven by multiplicative noise. The main…

We prove a center manifold theorem for rough partial differential equations (rough PDEs). The class of rough PDEs we consider contains as a key subclass reaction-diffusion equations driven by nonlinear multiplicative noise, where the…

In this work, we are interested in building the fully discrete scheme for stochastic fractional diffusion equation driven by fractional Brownian sheet which is temporally and spatially fractional with Hurst parameters $H_{1}, H_{2}…

We develop a numerical method for solving the acoustic wave equation in covariant form on staggered curvilinear grids in an energy conserving manner. The use of a covariant basis decomposition leads to a rotationally invariant scheme that…

In this paper we propose and analyze explicit space-time discrete numerical approximations for additive space-time white noise driven stochastic partial differential equations (SPDEs) with non-globally monotone nonlinearities such as the…

In this paper, we study a class of stochastic partial differential equations (SPDEs) driven by space-time fractional noises. Our method consists in studying first the nonlocal SPDEs and showing then the convergence of the family of these…

In this article, we analyse a stabilised equal-order finite element approximation for the Stokes equations on anisotropic meshes. In particular, we allow arbitrary anisotropies in a sub-domain, for example along the boundary of the domain,…