Optimization of mesh hierarchies in multilevel Monte Carlo samplers
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In this paper, we propose a semi-implicit approach for the time discretization of the Navier–Stokes equations with Variational Multiscale-Large Eddy Simulation turbulence modeling (VMS-LES). For the spatial approximation of the problem, we use the Finite E ...
We perform a general optimization of the parameters in the Multilevel Monte Carlo (MLMC) discretization hierarchy based on uniform discretization methods with general approximation orders and computational costs. Moreover, we discuss extensions to non-unif ...
Artists and architects often need to handle multiple constraints during design of physical constructions. We define a performative constraint as any constraint on design that is tied to the performance of the model--either during fabrication, construction, ...
In this article, we address the numerical solution of the Dirichlet problem for the three-dimensional elliptic Monge-Ampere equation using a least-squares/relaxation approach. The relaxation algorithm allows the decoupling of the differential operators fro ...
We propose a new selection rule for the coordinate selection in coordinate descent methods for huge-scale optimization. The efficiency of this novel scheme is provably better than the efficiency of uniformly random selection, and can reach the efficiency o ...
The numerical solution of partial differential equations (PDEs) depending on para- metrized or random input data is computationally intensive. Reduced order modeling techniques, such as the reduced basis methods, have been developed to alleviate this compu ...
MATHICSE2016
The significant progress that has been made in recent years both in hardware implementations and in numerical computing has rendered real-time optimization-based control a viable option when it comes to advanced industrial applications. At the same time, t ...
EPFL2018
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We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space of (multivariate and non-discrete) probability distribut ...
2018
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We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation with random data, where the random coefficient is parametrized by means of a countable sequence of terms in a ...
MATHICSE2015
,
We analyze the recent Multi-index Stochastic Collocation (MISC) method for computing statistics of the solution of a partial differential equation (PDE) with random data, where the random coefficient is parametrized by means of a countable sequence of term ...