相关论文: Penalty Ensembles for Navier-Stokes with Random In…
The chaotic nature of fluid flow and the uncertainties in initial conditions limit predictability. Small errors that occur in the initial condition can grow exponentially until they saturate at $\mathcal{O}$(1). Ensemble forecasting…
Penalty methods relax the incompressibility condition and uncouple velocity and pressure. Experience with them indicates that the velocity error is sensitive to the choice of penalty parameter $\epsilon$. So far, there is no effective \'a…
We propose novel ensemble calculation methods for Navier-Stokes equations subject to various initial conditions, forcing terms and viscosity coefficients. We establish the stability of the schemes under a CFL condition involving velocity…
Ensemble calculations are essential for systems with uncertain data but require substantial increase in computational resources. This increase severely limits ensemble size. To reach beyond current limits, we present a first-order…
A time-discretization of the stochastic incompressible Navier--Stokes problem by penalty method is analyzed. Some error estimates are derived, combined, and eventually arrive at a speed of convergence in probability of order 1/4 of the main…
The volume penalty method provides a simple, efficient approach for solving the incompressible Navier-Stokes equations in domains with boundaries or in the presence of moving objects. Despite the simplicity, the method is typically limited…
We consider settings for which one needs to perform multiple flow simulations based on the Navier-Stokes equations, each having different values for the physical parameters and/or different initial condition data, boundary conditions data,…
This paper aims to compare and evaluate various obstacle approximation techniques employed in the context of the steady incompressible Navier-Stokes equations. Specifically, we investigate the effectiveness of a standard volume penalization…
In this paper, we construct novel first- and second-order decoupled schemes for the Navier-Stokes equations based on the penalty method and the sequential regularization method (SRM), respectively. These schemes do not require the boundary…
In this paper, both semidiscrete and fully discrete finite element methods are analyzed for the penalized two-dimensional unsteady Navier-Stokes equations with nonsmooth initial data. First order backward Euler method is applied for the…
The paper introduces a finite element method for the incompressible Navier--Stokes equations posed on a closed surface $\Gamma\subset\R^3$. The method needs a shape regular tetrahedra mesh in $\mathbb{R}^3$ to discretize equations on the…
Feasibility pumps are highly effective primal heuristics for mixed-integer linear and nonlinear optimization. However, despite their success in practice there are only few works considering their theoretical properties. We show that…
In this paper, we consider the problem of minimizing a smooth function, given as finite sum of black-box functions, over a convex set. In order to advantageously exploit the structure of the problem, for instance when the terms of the…
In 1991, Ramshaw and Mesina proposed a novel synthesis of penalty methods and artificial compression methods. When the two were balanced they found the combination was 3-4 orders more accurate than either alone. This report begins the study…
This paper presents two algorithms for calculating an ensemble of solutions to laminar natural convection problems. The ensemble average is the most likely temperature distribution and its variance gives an estimate of prediction…
Constrained machine learning enables fairness-aware training, physics-informed neural networks, and integration of symbolic domain knowledge into statistical models. Despite its practical importance, no general method exists for the…
We propose a novel algorithm for solving non-convex, nonlinear equality-constrained finite-sum optimization problems. The proposed algorithm incorporates an additional sampling strategy for sample size update into the well-known framework…
In this paper, we propose sparsity-aware data-selective adaptive filtering algorithms with adjustable penalties. Prior work incorporates a penalty function into the cost function used in the optimization that originates the algorithms to…
A method of simultaneously optimizing both the structure of neural networks and the connection weights in a single training loop can reduce the enormous computational cost of neural architecture search. We focus on the probabilistic…
In this paper we present extensions of the schemes proposed in \cite{GM14} that lead to a decoupling of the velocity components in the momentum equation. The new schemes reduce the solution of the incompressible Navier-Stokes equations to a…