Related papers: Remarks on regularization by noise, convex integra…
We consider a slow passage through a point of loss of stability. If the passage is sufficiently slow, the dynamics are controlled by additive random disturbances, even if they are extremely small. We derive expressions for the `exit value'…
At the macroscopic scale, many important models of collective motion fall into the class of kinematic flows for which both velocity and diffusion terms depend only on particle density. When total particle numbers are fixed and finite,…
Effective stochastic equations for the continuous transitions of relativistic quantum fields inevitably contain multiplicative noise. We examine the effect of such noise in a numerical simulation of a temperature quench in a 1+1 dimensional…
The influence of small random perturbations on a deterministic dynamical system with a locally stable equilibrium is considered. The perturbed system is described by the It\^{o} stochastic differential equation. It is assumed that the noise…
Many problems in fluid dynamics are effectively modeled as Stokes flows - slow, viscous flows where the Reynolds number is small. Boundary integral equations are often used to solve these problems, where the fundamental solutions for the…
Regularization is a well studied problem in the context of neural networks. It is usually used to improve the generalization performance when the number of input samples is relatively small or heavily contaminated with noise. The…
We present general relativistic correction terms appearing in Newton's gravity to the second-order perturbations of cosmological fluids. In our previous work we have shown that to the second-order perturbations, the density and velocity…
We study the effect of Gaussian perturbations on a class of model hyperbolic partial differential equations with double symplectic characteristics in low spatial dimensions, extending some recent work in [5]. The coefficients of our partial…
We discuss the relation between three recent approaches of describing the dynamics and the spatial distribution of particles suspended in turbulent flows: phase-space singularities in the inertial particle dynamics (caustics), real-space…
Numerical approximation of a stochastic partial integro-differential equation driven by a space- time white noise is studied by truncating a series representation of the noise, with finite element method for spatial discretization and…
This paper studies least-square regression penalized with partly smooth convex regularizers. This class of functions is very large and versatile allowing to promote solutions conforming to some notion of low-complexity. Indeed, they force…
Most fluid flow problems that are vital in engineering applications involve at least one of the following features: turbulence, shocks, and/or material interfaces. While seemingly different phenomena, these flows all share continuous…
For optimizing a non-convex function in finite dimension, a method is to add Brownian noise to a gradient descent, allowing for transitions between basins of attractions of different minimizers. To adapt this for optimization over a space…
Motivated by the fact that in nature almost all phenomena behave randomly in some scales and deterministically in some other scales, we build up a framework suitable to tackle both deterministic and stochastic homogenization problems…
A method is provided for approximating random slow manifolds of a class of slow-fast stochastic dynamical systems. Thus approximate, low dimensional, reduced slow systems are obtained analytically in the case of sufficiently large time…
Some intriging connections between the properties of nonlinear noise driven systems and the nonlinear dynamics of a particular set of Hamilton's equation are discussed. A large class of Fokker-Planck Equations, like the Schr\"odinger…
Covariance of the resulting probabilities requires the "anti-Ito" sense. The corresponding Fokker-Planck equation is simplified and preserves important features of the case with a constant diffusion. Multiplicative noise can always be…
Recent studies have shown that many nonconvex machine learning problems satisfy a generalized-smooth condition that extends beyond traditional smooth nonconvex optimization. However, the existing algorithms are not fully adapted to such…
We introduce the Random Quadratic Form (RQF): a stochastic differential equation which formally corresponds to the gradient flow of a random quadratic functional on a sphere. While the one-point dynamics of the system is a Brownian motion…
In the Monte Carlo (MC) method statistical noise is usually present. Statistical noise may become dominant in the calculation of a distribution, usually by iteration, but is less Important in calculating integrals. The subject of the…