相关论文: Stochastic Curve Shortening Flow with Scale-Depend…

We revisit the well-known Curve Shortening Flow for immersed curves in the $d$-dimensional Euclidean space. We exploit a fundamental structure of the problem to derive a new global construction of a solution, that is, a construction that is…

We consider the problem of minimizing a convex function that is evolving according to unknown and possibly stochastic dynamics, which may depend jointly on time and on the decision variable itself. Such problems abound in the machine…

Measurements of radio signals induced by an astroparticle generating a cascade present a challenge because they are always superposed with an irreducible noise contribution. Quantifying these signals constitutes a non-trivial task,…

We adopt an input-output approach to analyze the effect of persistent white-in-time structured stochastic base flow perturbations on the mean-square properties of the linearized Navier-Stokes equations. Such base flow variations enter the…

We consider a stochastic perturbation of the $\alpha$-Navier-Stokes model. The stochastic perturbation is an additive space-time noise of trace class. Under a natural condition about the trace of operator $Q$ in front of the noise, we prove…

In this paper, we consider stochastic two-phase Stefan problem driven by general jump L\'evy noise. We first obtain the existence and uniqueness of the strong solution and then establish the ergodicity of the stochastic Stefan problem.…

In the machine learning literature stochastic gradient descent has recently been widely discussed for its purported implicit regularization properties. Much of the theory, that attempts to clarify the role of noise in stochastic gradient…

Using Stokesian dynamics simulations, we examine the flow of a monodisperse, neutrally buoyant, homogeneous suspension of non-Brownian solid spheres in simple shear, starting from a large number of independent hard-sphere distributions and…

New classes of stochastic differential equations can now be studied using rough path theory (e.g. Lyons et al. [LCL07] or Friz--Hairer [FH14]). In this paper we investigate, from a numerical analysis point of view, stochastic differential…

Diffusion models proved to be powerful models for generative speech enhancement. In recent SGMSE+ approaches, training involves a stochastic differential equation for the diffusion process, adding both Gaussian and environmental noise to…

The creation and subsequent evolution of marginally-unstable modes have been observed in a wide range of fusion devices. This behaviour has been successfully explained, for a single frequency shifting mode, in terms of phase-space…

We study the stochastic transport equation with globally $\beta$-H\"older continuous and bounded vector field driven by a non-degenerate pure-jump L\'evy noise of $\alpha$-stable type. Whereas the deterministic transport equation may lack…

We investigate the dynamics of linear perturbations in Keplerian flow under external stochastic force. To abstract from the details of flow structure and boundary conditions, we consider the problem in the shearing box approximation. An…

The effect of a small amount of noise on the standard mapping is considered. Whenever the standard mapping possesses accelerator modes (where the action increases approximately linearly with time), the diffusion coefficient contains a term…

The effect of viscosity and thermal conduction on the acoustics in a shear layer above an impedance wall is investigated numerically and asymptotically by solving the compressible linearised Navier-Stokes equations. It is found that…

We analyze the variance of stochastic gradients along negative curvature directions in certain non-convex machine learning models and show that stochastic gradients exhibit a strong component along these directions. Furthermore, we show…

Modeling and synthesizing image noise is an important aspect in many computer vision applications. The long-standing additive white Gaussian and heteroscedastic (signal-dependent) noise models widely used in the literature provide only a…

This paper is concerned with steady, fully developed motion of a Navier-Stokes fluid with shear-dependent viscosity in a curved pipe under a given axial pressure gradient. We establish existence and uniqueness results, derive appropriate…

This work is concerned with the dynamics of a class of slow-fast stochastic dynamical systems with non-Gaussian stable L\'evy noise with a scale parameter. Slow manifolds with exponentially tracking property are constructed, eliminating the…

We study a noise-induced bifurcation in the vicinity of the threshold by using a perturbative expansion of the order parameter, called the Poincar\'e-Lindstedt expansion. Each term of this series becomes divergent in the long time limit if…