Results 31 to 40 of about 545,959 (267)
On multilevel Monte Carlo methods for deterministic and uncertain hyperbolic systems [PDF]
Journal of Computational Physics, 2022 In this paper, we evaluate the performance of the multilevel Monte Carlo method (MLMC) for deterministic and uncertain hyperbolic systems, where randomness is introduced either in the modeling parameters or in the approximation algorithms. MLMC is a well
Junpeng Hu +3 more
semanticscholar +1 more source
Multilevel Markov Chain Monte Carlo [PDF]
SIAM Review, 2019 The authors are interested in uncertainty quantification in porous media flow with high-dimensional parameter spaces. This problem is often solved by Markov chain Monte Carlo methods, which have a prohibitively large computational cost. First, the authors propose a new multilevel Metropolis-Hastings algorithm and establish a complexity theorem that ...
Dodwell, T +3 more
openaire +4 more sources
Weak Error for Nested Multilevel Monte Carlo [PDF]
Methodology and Computing in Applied Probability, 2020 This article discusses MLMC estimators with and without weights, applied to nested expectations of the form E [f (E [F (Y, Z)|Y ])]. More precisely, we are interested on the assumptions needed to comply with the MLMC framework, depending on whether the payoff function f is smooth or not.
Giorgi, Daphné +2 more
openaire +3 more sources
MULTILEVEL MONTE CARLO ESTIMATORS FOR DERIVATIVE-FREE OPTIMIZATION UNDER UNCERTAINTY [PDF]
International Journal for Uncertainty Quantification, 2023 Optimization is a key tool for scientific and engineering applications, however, in the presence of models affected by uncertainty, the optimization formulation needs to be extended to consider statistics of the quantity of interest.
F. Menhorn +5 more
semanticscholar +1 more source
Multilevel Monte Carlo for solving POMDPs on-line [PDF]
The International Journal of Robotics Research, 2022 Planning under partial observability is essential for autonomous robots. A principled way to address such planning problems is the Partially Observable Markov Decision Process (POMDP). Although solving POMDPs is computationally intractable, substantial advancements have been achieved in developing approximate POMDP solvers in the past two decades ...
Marcus Hoerger +2 more
openaire +2 more sources
Algorithms, 2020 Civil engineering applications are often characterized by a large uncertainty on the material parameters. Discretization of the underlying equations is typically done by means of the Galerkin Finite Element method. The uncertain material parameter can be
Philippe Blondeel +5 more
doaj +1 more source
Multilevel Monte Carlo Approximation of Functions [PDF]
SIAM/ASA Journal on Uncertainty Quantification, 2018 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Krumscheid, Sebastian, Nobile, Fabio
openaire +3 more sources
Improved Efficiency of Multilevel Monte Carlo for Stochastic PDE through Strong Pairwise Coupling [PDF]
Journal of Scientific Computing, 2021 Multilevel Monte Carlo (MLMC) has become an important methodology in applied mathematics for reducing the computational cost of weak approximations.
N. Chada +3 more
semanticscholar +1 more source
Multilevel Monte Carlo learning
, 2021 In this work, we study the approximation of expected values of functional quantities on the solution of a stochastic differential equation (SDE), where we replace the Monte Carlo estimation with the evaluation of a deep neural network. Once the neural network training is done, the evaluation of the resulting approximating function is computationally ...
Gerstner, Thomas +3 more
openaire +2 more sources
Open Mathematics, 2022 Davie’s exact coupling technique for stochastic differential equations may be used to enhance the convergence of the multilevel Monte Carlo (MC) methodology.
Alnafisah Yousef
doaj +1 more source