Related papers: Multiple-scale stochastic processes: decimation, a…
Multistage stochastic optimization problems are, by essence, complex as their solutions are indexed both by stages and by uncertainties. Their large scale nature makes decomposition methods appealing, like dynamic programming which is a…
In {\em{Holm}, Proc. Roy. Soc. A 471 (2015)} stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics…
Stochastic hydrodynamics is a central tool in the study of first order phase transitions at a fundamental level. Combined with sophisticated free energy models, e.g. as developed in classical Density Functional Theory, complex processes…
Divergence-form operators with random coefficients homogenize over large scales. Over the last decade, an intensive research effort focused on turning this asymptotic statement into quantitative estimates. The goal of this note is to review…
In all but special circumstances, measurements of time-dependent processes reflect internal structures and correlations only indirectly. Building predictive models of such hidden information sources requires discovering, in some way, the…
High-quality nanomechanical oscillators can sensitively probe force, mass, or displacement in experiments bridging the gap between the classical and quantum domain. Dynamics of these stochastic systems is inherently determined by the…
We consider a system of differential equations in a fast long range dependent random environment and prove a homogenization theorem involving multiple scaling constants. The effective dynamics solves a rough differential equation, which is…
Stochastic treatments of magnetic resonance spectroscopy and optical spectroscopy require evaluations of functions like <exp(i int_0^t Q(s)ds)>, where t is time, Q(s) is the value of a stochastic process at time s, and the angular brackets…
Stochastic thermodynamics provides the framework to analyze thermodynamic laws and quantities along individual trajectories of small but fully observable systems. If the observable level fails to capture all relevant degrees of freedom,…
The 2-step staggered (also called leap-frog) time discretisation of linear 2nd-order Hamiltonian systems (typically linear elastodynamics in a stress-velocity form) is extended for a 3-step staggered discretisation applicable for systems…
Stochastic gradient descent is an optimisation method that combines classical gradient descent with random subsampling within the target functional. In this work, we introduce the stochastic gradient process as a continuous-time…
In modeling spatial processes, a second-order stationarity assumption is often made. However, for spatial data observed on a vast domain, the covariance function often varies over space, leading to a heterogeneous spatial dependence…
We analyze the asymptotic behavior of a multiscale problem given by a sequence of integral functionals subject to differential constraints conveyed by a constant-rank operator with two characteristic length scales, namely the film thickness…
This article develops a novel data assimilation methodology, addressing challenges that are common in real-world settings, such as severe sparsity of observations, lack of reliable models, and non-stationarity of the system dynamics. These…
Gradient descent methods and especially their stochastic variants have become highly popular in the last decade due to their efficiency on big data optimization problems. In this thesis we present the development of data sampling strategies…
Traditional models of wormlike chains in shear flows at finite temperature approximate the equation of motion via finite difference discretization (bead and rod models). We introduce here a new method based on a spectral representation in…
We discuss certain basic features of the equation-free (EF) approach to modeling and computation for complex/multiscale systems. We focus on links between the equation-free approach and tools from systems and control theory (design of…
This paper is the second in a series devoted to the study of Langevin systems subjected to a continuous time-delayed feedback control. The goal of our previous paper [Phys. Rev. E 91, 042114 (2015)] was to derive second-law-like…
Gradient normalization and soft clipping are two popular techniques for tackling instability issues and improving convergence of stochastic gradient descent (SGD) with momentum. In this article, we study these types of methods through the…
A system responding to a stochastic driving signal can be interpreted as computing, by means of its dynamics, an implicit model of the environmental variables. The system's state retains information about past environmental fluctuations,…