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The computational complexity of naive, sampling-based uncertainty quantification for 3D partial differential equations is extremely high. Multilevel approaches, such as multilevel Monte Carlo (MLMC), can reduce the complexity significantly,…

Computational Engineering, Finance, and Science · Computer Science 2016-07-13 Björn Gmeiner , Daniel Drzisga , Ulrich Ruede , Robert Scheichl , Barbara Wohlmuth

We investigate the applicability of the well-known multilevel Monte Carlo (MLMC) method to the class of density-driven flow problems, in particular the problem of salinisation of coastal aquifers. As a test case, we solve the uncertain…

Computational Engineering, Finance, and Science · Computer Science 2024-03-27 Dmitry Logashenko , Alexander Litvinenko , Raul Tempone , Ekaterina Vasilyeva , Gabriel Wittum

Multimodal distributions of some physics based model parameters are often encountered in engineering due to different situations such as a change in some environmental conditions, and the presence of some types of damage and nonlinearity.…

Computation · Statistics 2022-10-19 Felipe Igea , Alice Cicirello

Bayesian model comparison (BMC) offers a principled probabilistic approach to study and rank competing models. In standard BMC, we construct a discrete probability distribution over the set of possible models, conditional on the observed…

Machine Learning · Statistics 2023-02-22 Marvin Schmitt , Stefan T. Radev , Paul-Christian Bürkner

In modern engineering, computer simulations are a popular tool to analyse, design, and optimize systems. Furthermore, concepts of uncertainty and the related reliability analysis and robust design are of increasing importance. Hence, an…

Computation · Statistics 2017-05-12 R. Schöbi , B. Sudret

Multi-dimensional classification (MDC) can be employed in a range of applications where one needs to predict multiple class variables for each given instance. Many existing MDC methods suffer from at least one of inaccuracy, scalability,…

Machine Learning · Computer Science 2023-11-28 Vu-Linh Nguyen , Yang Yang , Cassio de Campos

Bayesian analysis often concerns an evaluation of models with different dimensionality as is necessary in, for example, model selection or mixture models. To facilitate this evaluation, transdimensional Markov chain Monte Carlo (MCMC)…

Methodology · Statistics 2018-08-13 Daniel W. Heck , Antony M. Overstall , Quentin F. Gronau , Eric-Jan Wagenmakers

As a nonlocal extension of continuum mechanics, peridynamics has been widely and effectively applied in different fields where discontinuities in the field variables arise from an initially continuous body. An important component of the…

Numerical Analysis · Mathematics 2021-09-22 Xiao Xu , Marta D'Elia , John T. Foster

Molecular dynamics (MD) has served as a powerful tool for designing materials with reduced reliance on laboratory testing. However, the use of MD directly to treat the deformation and failure of materials at the mesoscale is still largely…

Materials Science · Physics 2023-01-12 Huaiqian You , Xiao Xu , Yue Yu , Stewart Silling , Marta D'Elia , John Foster

The Multilevel Monte Carlo method is an efficient variance reduction technique. It uses a sequence of coarse approximations to reduce the computational cost in uncertainty quantification applications. The method is nowadays often considered…

Numerical Analysis · Mathematics 2018-06-15 Pieterjan Robbe , Dirk Nuyens , Stefan Vandewalle

Uncertainty analysis in the outcomes of model predictions is a key element in decision-based material design to establish confidence in the models and evaluate the fidelity of models. Uncertainty Propagation (UP) is a technique to determine…

Machine Learning · Computer Science 2023-02-13 Danial Khatamsaz , Vahid Attari , Raymundo Arroyave , Douglas L. Allaire

Bayesian inference involves the specification of a statistical model by a statistician or practitioner, with careful thought about what each parameter represents. This results in particularly interpretable models which can be used to…

Computation · Statistics 2019-08-07 Jonathan Law , Darren Wilkinson

In many real-world engineering systems, the performance or reliability of the system is characterised by a scalar parameter. The distribution of this performance parameter is important in many uncertainty quantification problems, ranging…

Methodology · Statistics 2022-10-03 Robert Millar , Jinglai Li , Hui Li

Monte Carlo methods play important part in modern statistical physics. The application of these methods suffer from two main difficulties.The first is caused by the relatively small number of particles that can participate in any numerical…

Statistical Mechanics · Physics 2007-05-23 A. Brandt , V. Ilyin

The subsurface flow is usually subject to uncertain porous media structures. In most cases, however, we only have partial knowledge about the porous media properties. A common approach is to model the uncertain parameters of porous media as…

Numerical Analysis · Mathematics 2019-10-11 Yang Liu , Jingfa Li , Shuyu Sun , Bo Yu

In a multi-fidelity setting, data are available from two sources, high- and low-fidelity. Low-fidelity data has larger size and can be leveraged to make more efficient inference about quantities of interest, e.g. the mean, for high-fidelity…

Methodology · Statistics 2026-03-12 Minji Kim , Brendan Brown , Vladas Pipiras

We consider parametric Markov decision processes (pMDPs) that are augmented with unknown probability distributions over parameter values. The problem is to compute the probability to satisfy a temporal logic specification with any concrete…

Logic in Computer Science · Computer Science 2022-12-08 Thom Badings , Murat Cubuktepe , Nils Jansen , Sebastian Junges , Joost-Pieter Katoen , Ufuk Topcu

Random field Monte Carlo (MC) reliability analysis is a robust stochastic method to determine the probability of failure. This method, however, requires a large number of numerical simulations demanding high computational costs. This paper…

Machine Learning · Computer Science 2022-04-14 Mohammad Aminpour , Reza Alaie , Navid Kardani , Sara Moridpour , Majidreza Nazem

A method for the multifidelity Monte Carlo (MFMC) estimation of statistical quantities is proposed which is applicable to computational budgets of any size. Based on a sequence of optimization problems each with a globally minimizing…

Numerical Analysis · Mathematics 2022-11-15 Anthony Gruber , Max Gunzburger , Lili Ju , Zhu Wang

Key questions that scientists and engineers typically want to address can be formulated in terms of predictive science. Questions such as: "How well does my computational model represent reality?", "What are the most important parameters in…

Mathematical Software · Computer Science 2012-02-07 Michael M. McKerns , Leif Strand , Tim Sullivan , Alta Fang , Michael A. G. Aivazis