Related papers: Cross-mode Stabilized Stochastic Shallow Water Sys…
The aim of this paper is to propose a systematic way to obtain convergent finite element schemes for the Darcy-Stokes flow problem by combining well-known mixed finite elements that are separately convergent for Darcy and Stokes problems.…
A priori analysis for a generalized local projection stabilized conforming finite element approximation of Darcy flow and Stokes problems is presented in this paper. A first-order conforming P1 finite element space is used to approximate…
Atmospheric models used for weather and climate prediction are traditionally formulated in a deterministic manner. In other words, given a particular state of the resolved scale variables, the most likely forcing from the sub-grid scale…
We describe a fully discrete mixed finite element method for the linearized rotating shallow water model, possibly with damping. While Crank-Nicolson time-stepping conserves energy in the absence of drag or forcing terms and is not subject…
In this article we consider one-dimensional random systems of hyperbolic conservation laws. We first establish existence and uniqueness of random entropy admissible solutions for initial value problems of conservation laws which involve…
We present a novel approach for solving the shallow water equations using a discontinuous Galerkin spectral element method. The method we propose has three main features. First, it enjoys a discrete well-balanced property, in a spirit…
We investigate the propagation of uncertainties in the Aw-Rascle-Zhang model, which belongs to a class of second order traffic flow models described by a system of nonlinear hyperbolic equations. The stochastic quantities are expanded in…
Element Method. The Finite Volume Method guarantees local and global mass conservation. A property not satisfied by the Finite Volume Method. On the down side, the Finite Volume Method requires non trivial modifications to attain high order…
In the Reduced Basis approximation of Stokes and Navier-Stokes problems, the Galerkin projection on the reduced spaces does not necessarily preserved the inf-sup stability even if the snapshots were generated through a stable full order…
This paper proposes a model predictive controller for discrete-time linear systems with additive, possibly unbounded, stochastic disturbances and subject to chance constraints. By computing a polytopic probabilistic positively invariant set…
Chaotic systems pose fundamental challenges for data-driven dynamics discovery, as small modeling errors lead to exponentially growing trajectory discrepancies. Since exact long-term prediction is unattainable, it is natural to ask what a…
In recent work, the authors have developed a generic methodology for calibrating the noise in fluid dynamics stochastic partial differential equations where the stochasticity was introduced to parametrize subgrid-scale processes. The…
Stochastic Galerkin finite element method (SGFEM) provides an efficient alternative to traditional sampling methods for the numerical solution of linear elliptic partial differential equations with parametric or random inputs. However,…
Stochastic unit commitment models typically handle uncertainties in forecast demand by considering a finite number of realizations from a stochastic process model for loads. Accurate evaluations of expectations or higher moments for the…
A surrogate model that accurately predicts distribution system voltages is crucial for reliable smart grid planning and operation. This letter proposes a fixed-point data-driven surrogate modeling method that employs a limited dataset to…
In this article we present a general framework for non-concave robust stochastic control problems under model uncertainty in a discrete time finite horizon setting. Our framework allows to consider a variety of different path-dependent…
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…
Control of complex turbulent dynamical systems involving strong nonlinearity and high degrees of internal instability is an important topic in practice. Different from traditional methods for controlling individual trajectories, controlling…
We propose a novel data-driven stochastic model predictive control framework for uncertain linear systems with noisy output measurements. Our approach leverages multi-step predictors to efficiently propagate uncertainty, ensuring chance…
We develop a stochastic parametrization, based on a `simple' deterministic model for the dynamics of steady longshore currents, that produces ensembles that are statistically consistent with field observations of these currents. Unlike…