Related papers: Geometry, mixing properties and hypocoercivity of …

Data-driven emulation of nonlinear dynamics is challenging due to long-range skill decay that often produces physically unrealistic outputs. Recent advances in generative modeling aim to address these issues by providing uncertainty…

Stochastic gradient algorithms are often unstable when applied to functions that do not have Lipschitz-continuous and/or bounded gradients. Gradient clipping is a simple and effective technique to stabilize the training process for problems…

Semilinear hyperbolic stochastic partial differential equations (SPDEs) find widespread applications in the natural and engineering sciences. However, the traditional Gaussian setting may prove too restrictive, as phenomena in mathematical…

To obtain explicit understanding of the behavior of dynamical systems, geometrical methods and slow-fast analysis have proved to be highly useful. Such methods are standard for smooth dynamical systems, and increasingly used for continuous,…

Mesoscale simulations of woven composites using parameterized analytical geometries offer a way to connect constituent material properties and their geometric arrangement to effective composite properties and performance. However, the…

We study stochastic motion under a nonlinear frictional force that levels off with increasing velocity. Specifically, our frictional force is of the so-called Coulomb-tanh type. At small speed, it increases approximately linearly with…

Understanding posterior contraction behavior in Bayesian hierarchical models is of fundamental importance, but progress in this question is relatively sparse in comparison to the theory of density estimation. In this paper, we study two…

We consider a simple model for the fluctuating hydrodynamics of a flexible polymer in dilute solution, demonstrating geometric ergodicity for a pair of particles that interact with each other through a nonlinear spring potential while being…

We consider the homogenisation of the Stokes equations in a porous medium which is evolving in time. At the interface of the pore space and the solid part, we prescribe an inhomogeneous Dirichlet boundary condition, which enables to model a…

In this paper we formulate a geometric theory of the mechanics of growing solids. Bulk growth is modeled by a material manifold with an evolving metric. Time dependence of metric represents the evolution of the stress-free (natural)…

Convergence of an adaptive collocation method for the stationary parametric diffusion equation with finite-dimensional affine coefficient is shown. The adaptive algorithm relies on a recently introduced residual-based reliable a posteriori…

We propose some new mixed finite element methods for the time dependent stochastic Stokes equations with multiplicative noise, which use the Helmholtz decomposition of the driving multiplicative noise. It is known [16] that the pressure…

Many important properties of granular fluids can be represented by a system of hard spheres with inelastic collisions. Traditional methods of nonequilibrium statistical mechanics are effective for analysis and description of the inelastic…

We experimentally study a piezoelectric energy harvester driven by broadband random vibrations. We show that a linear model, consisting of an underdamped Langevin equation for the dynamics of the tip mass, electromechanically coupled with a…

Denoising diffusions are state-of-the-art generative models exhibiting remarkable empirical performance. They work by diffusing the data distribution into a Gaussian distribution and then learning to reverse this noising process to obtain…

The last decade has seen the success of stochastic parameterizations in short-term, medium-range and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to better represent model inadequacy…

Matrix stiffness expressions are derived for the particle movements in an assembly of rigid granules having compliant contacts. The derivations include stiffness terms that arise from the particle shapes at their contacts. These geometric…

In this paper homogenization of a mathematical model for biomechanics of a plant tissue with randomly distributed cells is considered. Mechanical properties of a plant tissue are modelled by a strongly coupled system of…

We consider the construction of the stochastic moment matrices that appear in the typical elliptic diffusion problem considered in the setting of stochastic Galerkin finite element method (sGFEM). Algorithms for the efficient construction…

We study numerical methods for sampling probability measures in high dimension where the underlying model is only approximately identified with a gradient system. Extended stochastic dynamical methods are discussed which have application to…