Related papers: Compressible fluid motion with uncertain data
We consider stochastic programs conditional on some covariate information, where the only knowledge of the possible relationship between the uncertain parameters and the covariates is reduced to a finite data sample of their joint…
Many large scale problems in computational fluid dynamics such as uncertainty quantification, Bayesian inversion, data assimilation and PDE constrained optimization are considered very challenging computationally as they require a large…
In this paper, an optimization problem with uncertain constraint coefficients is considered. Possibility theory is used to model the uncertainty. Namely, a joint possibility distribution in constraint coefficient realizations, called…
We analyze the accuracy and sample complexity of variational Monte Carlo approaches to simulate the dynamics of many-body quantum systems classically. By systematically studying the relevant stochastic estimators, we are able to: (i) prove…
A proposal for a calculational program in fluid turbulence is presented. It is proposed that the fluid probability density functional has an attractor for its time-evolution, just as the dynamical system itself has. The evolution of the…
Modern techniques for physical simulations rely on numerical schemes and mesh-refinement methods to address trade-offs between precision and complexity, but these handcrafted solutions are tedious and require high computational power.…
We prove the existence of a weak solution to the equations describing the inertial motions of a coupled system constituted by a rigid body containing a viscous compressible fluid. We then provide a weak-strong uniqueness result that allows…
In this paper we consider a stochastic heavy-ball method for solving linear ill-posed inverse problems. With suitable choices of the step-sizes and the momentum coefficients, we establish the regularization property of the method under {\it…
We investigate the long-time behavior of solutions to a stochastically forced one-dimensional Navier-Stokes system, describing the motion of a compressible viscous fluid, in the case of linear pressure law. We prove existence of an…
In this paper we introduce and discuss numerical schemes for the approximation of kinetic equations for flocking behavior with phase transitions that incorporate uncertain quantities. This class of schemes here considered make use of a…
Uncertainty quantification provides quantitative measures on the reliability of candidate solutions of ill-posed inverse problems. Due to their sequential nature, Monte Carlo sampling methods require large numbers of sampling steps for…
Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady state performance of the…
We introduce a stochastic traffic flow model to describe random traffic accidents on a single road. The model is a piecewise deterministic process incorporating traffic accidents and is based on a scalar conservation law with…
A machine-learning strategy for investigating the stability of fluid flow problems is proposed herein. The goal is to provide a simple yet robust methodology to find a nonlinear mapping from the parametric space to an indicator representing…
We propose a data-driven, coarse-graining formulation in the context of equilibrium statistical mechanics. In contrast to existing techniques which are based on a fine-to-coarse map, we adopt the opposite strategy by prescribing a…
A kinetic-fluid model describing the evolutions of disperse two-phase flows is considered. The model consists of the Vlasov-Fokker-Planck equation for the particles (disperse phase) coupled with the compressible Navier-Stokes equations for…
This paper presents a probabilistic approach to represent and quantify model-form uncertainties in the reduced-order modeling of complex systems using operator inference techniques. Such uncertainties can arise in the selection of an…
We introduce a physically relevant stochastic representation of the rotating shallow water equations. The derivation relies mainly on a stochastic transport principle and on a decomposition of the fluid flow into a large-scale component and…
The study of the dynamics of the size of a population via mathematical modelling is a problem of interest and widely studied. Traditionally, continuous deterministic methods based on differential equations have been used to deal with this…
Any performance analysis based on stochastic simulation is subject to the errors inherent in misspecifying the modeling assumptions, particularly the input distributions. In situations with little support from data, we investigate the use…