Related papers: Predicting Uncertainty in Geometric Fluid Mechanic…

Numerical simulators are essential tools in the study of natural fluid-systems, but their performance often limits application in practice. Recent machine-learning approaches have demonstrated their ability to accelerate spatio-temporal…

We present a numerical investigation of stochastic transport in ideal fluids. According to Holm (Proc Roy Soc, 2015) and Cotter et al. (2017), the principles of transformation theory and multi-time homogenisation, respectively, imply a…

Understanding the dynamics of material objects advected by turbulent flows is a long standing question in fluid dynamics. In this perspective article we focus on the characterization of the statistical properties of non-interacting…

Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…

Geometric Hydrodynamics has flourished ever since the celebrated 1966 paper of V. Arnold. In this paper we present a collection of open problems along with several new constructions in fluid dynamics and a concise survey of recent…

This study evaluates data-driven models from a dynamical system perspective, such as unstable fixed points, periodic orbits, chaotic saddle, Lyapunov exponents, manifold structures, and statistical values. We find that these dynamical…

The fluctuations in nonequilibrium systems are under intense theoretical and experimental investigation. Topical ``fluctuation relations'' describe symmetries of the statistical properties of certain observables, in a variety of models and…

Recently, the theoretical framework of stochastic thermodynamics has been revealed to be useful for macroscopic systems. However, despite its conceptual and practical importance, the connection to hydrodynamics has yet to be explored. In…

Models for fluid deformable surfaces provide valid theories to describe the dynamics of thin fluidic sheets of soft materials. To use such models in morphogenesis and development requires to incorporate active forces. We consider active…

Generative models have demonstrated remarkable success in domains such as text, image, and video synthesis. In this work, we explore the application of generative models to fluid dynamics, specifically for turbulence simulation, where…

We consider linear hyperbolic balance law that describe gas flow. Stochastic influences are introduced by series of orthogonal functions. A deterministic stabilization concept, which makes deviations at steady states decay exponentially…

In stochastic decision problems, one often wants to estimate the underlying probability measure statistically, and then to use this estimate as a basis for decisions. We shall consider how the uncertainty in this estimation can be…

Invariant manifolds provide the geometric structures for describing and understanding dynamics of nonlinear systems. The theory of invariant manifolds for both finite and infinite dimensional autonomous deterministic systems, and for…

A classic approach in dynamical systems is to use particular geometric structures to deduce statistical properties, for example the existence of invariant measures with stochastic-like behaviour such as large deviations or decay of…

We propose a multiscale approach for predicting quantities in dynamical systems which is explicitly structured to extract information in both fine-to-coarse and coarse-to-fine directions. We envision this method being generally applicable…

Many applications of porous media research involves high pressures and, correspondingly, exchange of thermal energy between the fluid and the matrix. While the system is relatively well understood for the case of non-moving porous media,…

Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are, however, difficult to characterize. Here, we…

We present a mechanistic model for a Newtonian fluid called fluid particle dynamics. By analyzing the concept of ``fluid particle'' from the point of view of a Voronoi tessellation of a molecular fluid, we propose an heuristic derivation of…

We present here a new stochastic modelling in the constitution of fluid flow reduced-order models. This framework introduces a spatially inhomogeneous random field to represent the unresolved small-scale velocity component. Such a…

Stochastic hydrodynamics provides a dynamical framework for the evolution of fluctuations in heavy-ion collisions, but poses significant challenges in numerical simulations. We present an algorithm for the simulation of non-relativistic…