Related papers: Stochastic analysis of different rough surfaces

This paper is concerned with the Fokker-Planck (FP) description of classical stochastic systems with discrete time delay. The non-Markovian character of the corresponding Langevin dynamics naturally leads to a coupled infinite hierarchy of…

It is shown that superpositions of path integrals with arbitrary Hamiltonians and different scaling parameters v ("variances") obey the Chapman-Kolmogorov relation for Markovian processes if and only if the corresponding smearing…

We propose a multilevel Markov chain Monte Carlo (MCMC) method for the Bayesian inference of random field parameters in PDEs using high-resolution data. Compared to existing multilevel MCMC methods, we additionally consider level-dependent…

Molecular dynamics are extremely complex, yet understanding the slow components of their dynamics is essential to understanding their macroscopic properties. To achieve this, one models the molecular dynamics as a stochastic process and…

We compare three random field discretization strategies for probabilistic identification of spatially varying material parameters in high-resolution finite element models. These strategies are (i) the Karhunen-Lo\`eve expansion, (ii) a…

We propose a method to obtain phase portraits for stochastic systems. Starting from the Fokker-Planck equation, we separate the dynamics into a convective and a diffusive part. We show that stable and unstable fixed points of the convective…

We study a numerical method to compute probability density functions of solutions of stochastic differential equations. The method is sometimes called the numerical path integration method and has been shown to be fast and accurate in…

Ferroic domain walls are known to display the characteristic scaling properties of self-affine rough interfaces. Different methods have been used to extract roughness information in ferroelectric and ferromagnetic materials. Here, we review…

These lecture notes present some new concentration inequalities for Feynman-Kac particle processes. We analyze different types of stochastic particle models, including particle profile occupation measures, genealogical tree based evolution…

The large time dynamics of a periodically driven Fokker-Planck process possessing several metastable states is investigated. At weak noise transitions between the metastable states are rare. Their dynamics then represent a discrete…

This paper formed part of a preliminary research report for a risk consultancy and academic research. Stochastic Programming models provide a powerful paradigm for decision making under uncertainty. In these models the uncertainties are…

For modelling geophysical systems, large-scale processes are described through a set of coarse-grained dynamical equations while small-scale processes are represented via parameterizations. This work proposes a method for identifying the…

At present, most surface-quality prediction methods can only perform single-task prediction which results in under-utilised datasets, repetitive work and increased experimental costs. To counter this, the authors propose a Bayesian…

Machine learning techniques not only offer efficient tools for modelling dynamical systems from data, but can also be employed as frontline investigative instruments for the underlying physics. Nontrivial information about the original…

Rough stochastic differential equations (rough SDEs), recently introduced by Friz, Hocquet and L\^e in arXiv:2106.10340, have emerged as a versatile tool to study "doubly" SDEs under partial conditioning (with motivation from pathwise…

We propose a new algorithm---Stochastic Proximal Langevin Algorithm (SPLA)---for sampling from a log concave distribution. Our method is a generalization of the Langevin algorithm to potentials expressed as the sum of one stochastic smooth…

In this paper we consider a new probability sampling methods based on Langevin diffusion dynamics to resolve the problem of existing Monte Carlo algorithms when draw samples from high dimensional target densities. We extent…

We study a class of multi-stage stochastic programs, which incorporate modeling features from Markov decision processes (MDPs). This class includes structured MDPs with continuous action and state spaces. We extend policy graphs to include…

Efficient and accurate integration of stochastic (partial) differential equations with multiplicative noise can be obtained through a split-step scheme, which separates the integration of the deterministic part from that of the stochastic…

Hyper-spectral data can be analyzed to recover physical properties at large planetary scales. This involves resolving inverse problems which can be addressed within machine learning, with the advantage that, once a relationship between…