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EXTREME LEARNING MACHINES FOR VARIANCE-BASED GLOBAL SENSITIVITY ANALYSIS Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2024-03-01 John Darges, Alen Alexanderian, Pierre Gremaud
Variance-based global sensitivity analysis (GSA) can provide a wealth of information when applied to complex models. A well-known Achilles’ heel of this approach is its computational cost which often renders it unfeasible in practice. An appealing alternative is to analyze instead the sensitivity of a surrogate model with the goal of lowering computational costs while maintaining sufficient accuracy
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Analysis of the Challenges in Developing Sample-Based Multi-fidelity Estimators for Non-deterministic Models Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2024-03-01 Bryan Reuter, Gianluca Geraci, Timothy Wildey
Multifidelity (MF) Uncertainty Quantification (UQ) seeks to leverage and fuse information from a collection of models to achieve greater statistical accuracy with respect to a single-fidelity counterpart, while maintaining an efficient use of computational resources. Despite many recent advancements in MF UQ, several challenges remain and these often limit its practical impact in certain application
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Application of global sensitivity analysis for identification of probabilistic design spaces Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2024-02-01 Sergei Kucherenko, Dimitris Giamalakis, Nilay Shah
The design space (DS) is defined as the combination of materials and process conditions, which provides assurance of quality for a pharmaceutical product. A model-based approach to identify a probability-based DS requires costly simulations across the entire process parameter space (certain) and the uncertain model parameter space. We demonstrate that application of global sensitivity analysis (GSA)
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Stochastic Galerkin method and port-Hamiltonian form for linear first-order ordinary differential equations Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2024-02-01 Roland Pulch, Olivier Sète
We consider linear first-order systems of ordinary differential equations (ODEs) in port-Hamiltonian (pH) form. Physical parameters are remodelled as random variables to conduct an uncertainty quantification. A stochastic Galerkin projection yields a larger deterministic system of ODEs, which does not exhibit a pH form in general. We apply transformations of the original systems such that the stochastic
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UNCERTAINTY QUANTIFICATION AND GLOBAL SENSITIVITY ANALYSIS OF SEISMIC FRAGILITY CURVES USING KRIGING Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2024-01-01 Clement Gauchy, C. Feau, Josselin Garnier
Seismic fragility curves have been introduced as key components of seismic probabilistic risk assessment studies. They express the probability of failure of mechanical structures conditional to a seismic intensity measure and must take into account various sources of uncertainties, the so-called epistemic uncertainties (i.e., coming from the uncertainty on the mechanical parameters of the structure)
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DECISION THEORETIC BOOTSTRAPPING Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2024-01-01 Peyman Tavallali, Hamed Hamze Bajgiran, Danial J. Esaid, Kun Wu
The design and testing of supervised machine learning models combine two fundamental distributions: (1) the training data distribution and (2) the testing data distribution. Although these two distributions are identical and identifiable when the data set is infinite, they are imperfectly known when the data are finite (and possibly corrupted), and this uncertainty must be taken into account for robust
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MODEL ERROR ESTIMATION USING PEARSON SYSTEM WITH APPLICATION TO NONLINEAR WAVES IN COMPRESSIBLE FLOWS Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2024-01-01 Ferdinand Uilhoorn
In data assimilation, the description of the model error uncertainty is of the utmost importance because, when incorrectly defined, it may lead to information loss about the real state of the system. In this work, we proposed a novel approach that finds the optimal distribution for describing the model error uncertainty within a particle filtering framework. The method was applied to nonlinear waves
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A DOMAIN-DECOMPOSED VAE METHOD FOR BAYESIAN INVERSE PROBLEMS Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2024-01-01 Zhihang Xu, Yingzhi Xia, Qifeng Liao
Bayesian inverse problems are often computationally challenging when the forward model is governed by complex partial differential equations (PDEs). This is typically caused by expensive forward model evaluations and highdimensional parameterization of priors. This paper proposes a domain-decomposed variational autoencoder Markov chain Monte Carlo (DD-VAE-MCMC) method to tackle these challenges simultaneously
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MULTILEVEL MONTE CARLO ESTIMATORS FOR DERIVATIVE-FREE OPTIMIZATION UNDER UNCERTAINTY Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2024-01-01 Friedrich Menhorn, Gianluca Geraci, D. Thomas Seidl, Youssef M. Marzouk, Michael S. Eldred, Hans-Joachim Bungartz
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. Optimization under uncertainty (OUU) deals with this endeavor and requires uncertainty quantification analyses at several design locations; i.e., its overall computational
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HYPERDIFFERENTIAL SENSITIVITY ANALYSIS IN THE CONTEXT OF BAYESIAN INFERENCE APPLIED TO ICE-SHEET PROBLEMS Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2024-01-01 William Reese, Joseph Hart, Bart van Bloemen Waanders, Mauro Perego, John D. Jakeman, Arvind K. Saibaba
Inverse problems constrained by partial differential equations (PDEs) play a critical role in model development and calibration. In many applications, there are multiple uncertain parameters in a model which must be estimated. Although the Bayesian formulation is attractive for such problems, computational cost and high dimensionality frequently prohibit a thorough exploration of the parametric uncertainty
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MORE POWERFUL HSIC-BASED INDEPENDENCE TESTS, EXTENSION TO SPACE-FILLING DESIGNS AND FUNCTIONAL DATA Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2024-01-01 Mohamed Reda El Amri, Amandine Marrel
The Hilbert-Schmidt independence criterion (HSIC) is a dependence measure based on reproducing kernel Hilbert spaces. This measure can be used for the global sensitivity analysis of numerical simulators whose objective is to identify the most influential inputs on the output(s) of the code. For this purpose, HSIC-based sensitivity measures and independence tests can be used for the ranking and screening
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LIKELIHOOD AND DEPTH-BASED CRITERIA FOR COMPARING SIMULATION RESULTS WITH EXPERIMENTAL DATA, IN SUPPORT OF VALIDATION OF NUMERICAL SIMULATORS Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2024-01-01 Amandine Marrel, H. Velardo, A. Bouloré
Within the framework of best-estimate-plus-uncertainty approaches, the assessment of model parameter uncertainties, associated with numerical simulators, is a key element in safety analysis. The results (or outputs) of the simulation must be compared and validated against experimental values, when such data are available. This validation step, as part of the broader verification, validation, and uncertainty
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A DIMENSION-ADAPTIVE COMBINATION TECHNIQUE FOR UNCERTAINTY QUANTIFICATION Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2024-01-01 Michael Griebel, Uta Seidler
We present an adaptive algorithm for the computation of quantities of interest involving the solution of a stochastic elliptic partial differential equation, where the diffusion coefficient is parametrized by means of a Karhunen-Loève expansion. The approximation of the equivalent parametric problem requires a restriction of the countably infinite-dimensional parameter space to a finite-dimensional
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HYPER-DIFFERENTIAL SENSITIVITY ANALYSIS FOR NONLINEAR BAYESIAN INVERSE PROBLEMS Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2024-01-01 Isaac Sunseri, Alen Alexanderian, Joseph Hart, Bart van Bloemen Waanders
We consider hyper-differential sensitivity analysis (HDSA) of nonlinear Bayesian inverse problems governed by partial differential equations (PDEs) with infinite-dimensional parameters. In previous works, HDSA has been used to assess the sensitivity of the solution of deterministic inverse problems to additional model uncertainties and also different types of measurement data. In the present work,
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A BAYESIAN NEURAL NETWORK APPROACH TO MULTI-FIDELITY SURROGATE MODELING Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2024-01-01 Baptiste Kerleguer, Claire Cannamela, Josselin Garnier
This paper deals with surrogate modeling of a computer code output in a hierarchical multi-fidelity context, i.e., when the output can be evaluated at different levels of accuracy and computational cost. Using observations of the output at low- and high-fidelity levels, we propose a method that combines Gaussian process (GP) regression and the Bayesian neural network (BNN), called the GPBNN method
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LONG SHORT-TERM RELEVANCE LEARNING Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2024-01-01 Bram P. van de Weg, L. Greve, B. Rosic
To incorporate sparsity knowledge as well as measurement uncertainties in the traditional long short-term memory (LSTM) neural networks, an efficient relevance vector machine algorithm is introduced to the network architecture. The proposed scheme automatically determines relevant neural connections and adapts accordingly, in contrast to the classical LSTM solution. Due to its flexibility, the new
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NESTED OPTIMAL UNCERTAINTY QUANTIFICATION FOR AN EFFICIENT INCORPORATION OF RANDOM FIELDS−APPLICATION TO SHEET METAL FORMING Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2024-01-01 Niklas Miska, Steffen Freitag, Daniel Balzani
In this work, a new method is presented to quantify the sharpest bounds on the probability of failure while including local variations of properties in terms of random fields. The method is based on the extended optimal uncertainty quantification (OUQ) for polymorphic uncertainties. Therein, a special focus is on the incorporation of aleatory as well as epistemic uncertainties without the requirement
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BAYESIAN CALIBRATION WITH ADAPTIVE MODEL DISCREPANCY Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2024-01-01 Nicolas Leoni, Olivier Le Maître, Maria-Giovanna Rodio, Pietro Marco Congedo
We investigate a computer model calibration technique inspired by the well-known Bayesian framework of Kennedy and O'Hagan (KOH). We tackle the full Bayesian formulation where model parameter and model discrepancy hyperparameters are estimated jointly and reduce the problem dimensionality by introducing a functional relationship that we call the full maximum a posteriori (FMP) method. This method also
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IMPROVING ACCURACY AND COMPUTATIONAL EFFICIENCY OF OPTIMAL DESIGN OF EXPERIMENTS VIA GREEDY BACKWARD APPROACH Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2024-01-01 Mehdi Taghizadeh, Dongbin Xiu, Negin Alemazkoor
Nonintrusive least-squares-based polynomial chaos expansion (PCE) techniques have attracted increasing attention among researchers for simple yet efficient surrogate constructions. Different sampling approaches, including optimal design of experiments (DoEs), have been developed to facilitate the least-squares-based PCE construction by reducing the number of required training samples. DoEs mainly include
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Quantifying uncertain system outputs via the multi-level Monte Carlo method --- distribution and robustness measures Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2023-04-01 Quentin Ayoul-Guilmard, Sundar Ganesh, Sebastian Krumscheid, Fabio Nobile
In this work, we consider the problem of estimating the probability distribution, the quantile or the conditional expectation above the quantile, the so called CVaR, of output quantities of complex random differential models by the MLMC method. We follow the approach of [1], which recasts the estimation of the above quantities to the computation of suitable parametric expectations. In this work, we
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UNBIASED ESTIMATION OF THE VANILLA AND DETERMINISTIC ENSEMBLE KALMAN−BUCY FILTERS Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2023-01-01 Miguel Alvarez, Neil K. Chada, Ajay Jasra
In this paper, we consider the development of unbiased estimators for the ensemble Kalman−Bucy filter (EnKBF). The EnKBF is a continuous-time filtering methodology, which can be viewed as a continuous-time analog of the famous discrete-time ensemble Kalman filter. Our unbiased estimators will be motivated from recent work (Rhee and Glynn, Oper. Res., 63:1026−1053, 2015) which introduces randomization
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SENSITIVITY ANALYSIS WITH CORRELATED INPUTS: COMPARISON OF INDICES FOR THE LINEAR CASE Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2023-01-01 Jean-Baptiste Blanchard
The objective of a global sensitivity analysis is to provide indices to rank the importance of each and every system input when considering the impact on a given system output. This paper discusses a few of the methods proposed throughout the literature when dealing with a linear model for which part of or all the input variables cannot be considered independently. The aim here is to review methods
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GLOBAL SENSITIVITY ANALYSIS USING DERIVATIVE-BASED SPARSE POINCARÉ CHAOS EXPANSIONS Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2023-01-01 Nora Lüthen, Olivier Roustant, Fabrice Gamboa, Bertrand Iooss, Stefano Marelli, Bruno Sudret
Variance-based global sensitivity analysis, in particular Sobol' analysis, is widely used for determining the importance of input variables to a computational model. Sobol' indices can be computed cheaply based on spectral methods like polynomial chaos expansions (PCE). Another choice are the recently developed Poincare chaos expansions (PoinCE), whose orthonormal tensor-product basis is generated
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DISCREPANCY MODELING FOR MODEL CALIBRATION WITH MULTIVARIATE OUTPUT Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2023-01-01 Andrew White, Sankaran Mahadevan
This paper explores the application of the Kennedy and O'Hagan (KOH) Bayesian framework to the calibration of physics models with multivariate outputs by formulating the problem in a dimension-reduced subspace. The approach in the KOH framework is to calibrate the physics model parameters simultaneously to the parameters of an additive discrepancy (model error) function. It is a known issue that such
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UNCERTAINTY QUANTIFICATION BY GAUSSIAN RANDOM FIELDS FOR POINT-LIKE EMISSIONS FROM SATELLITE OBSERVATIONS Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2023-01-01 Teemu Härkönen, Anu-Maija Sundström, Johanna Tamminen, Janne Hakkarainen, Esa Vakkilainen, Heikki Haario
We propose a statistical approach to estimate emissions of isolated pointlike sources by NO2 tropospheric column concentrations satellite observations. The approach is data driven; in addition to the satellite measurements it only uses available wind data and a rudimentary model for the NOx chemistry. We construct interpolated fields of the satellite observations using Gaussian random fields, which
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COMBINED DATA AND DEEP LEARNING MODEL UNCERTAINTIES: AN APPLICATION TO THE MEASUREMENT OF SOLID FUEL REGRESSION RATE Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2023-01-01 Georgios Georgalis, Kolos Retfalvi, Paul E. Desjardin, Abani Patra
In complex physical process characterization, such as the measurement of the regression rate for solid hybrid rocket fuels, where both the observation data and the model used have uncertainties originating from multiple sources, combining these in a systematic way for quantities of interest (QoI) remains a challenge. In this paper, we present a forward propagation uncertainty quantification (UQ) process
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AN ADAPTIVE STRATEGY FOR SEQUENTIAL DESIGNS OF MULTILEVEL COMPUTER EXPERIMENTS Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2023-01-01 Ayao Ehara, Serge Guillas
Investigating uncertainties in computer simulations can be prohibitive in terms of computational costs, since the simulator needs to be run over a large number of input values. Building an emulator, i.e., a statistical surrogate model of the simulator constructed using a design of experiments made of a comparatively small number of evaluations of the forward solver, greatly alleviates the computational
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A STOCHASTIC DOMAIN DECOMPOSITION AND POST-PROCESSING ALGORITHM FOR EPISTEMIC UNCERTAINTY QUANTIFICATION Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2023-01-01 Mahadevan Ganesh, S. C. Hawkins, Alexandre M. Tartakovsky, Ramakrishna Tipireddy
Partial differential equations (PDEs) are fundamental for theoretically describing numerous physical processes that are based on some input fields in spatial configurations. Understanding the physical process, in general, requires computational modeling of the PDE in bounded/unbounded regions. Uncertainty in the computational model manifests through lack of precise knowledge of the input field or configuration
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HIGH-DIMENSIONAL STOCHASTIC DESIGN OPTIMIZATION UNDER DEPENDENT RANDOM VARIABLES BY A DIMENSIONALLY DECOMPOSED GENERALIZED POLYNOMIAL CHAOS EXPANSION Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2023-01-01 Dongjin Lee, Sharif Rahman
Newly restructured generalized polynomial chaos expansion (GPCE) methods for high-dimensional design optimization in the presence of input random variables with arbitrary, dependent probability distributions are reported. The methods feature a dimensionally decomposed GPCE (DD-GPCE) for statistical moment and reliability analyses associated with a high-dimensional stochastic response; a novel synthesis
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UNCERTAINTY QUANTIFICATION OF WATERFLOODING IN OIL RESERVOIRS COMPUTATIONAL SIMULATIONS USING A PROBABILISTIC LEARNING APPROACH Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2023-01-01 Jeferson Osmar Almeida, Fernando A. Rochinha
In the present paper, we propose an approach based on probabilistic learning for uncertainty quantification of the water-flooding processes in oil reservoir simulations, considering geological and economic uncertainties and multiple quantities of interest (QoIs). We employ the probabilistic learning on manifolds (PLoM) method, which has achieved success in many different applications. This methodology
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CONTROL VARIATE POLYNOMIAL CHAOS: OPTIMAL FUSION OF SAMPLING AND SURROGATES FOR MULTIFIDELITY UNCERTAINTY QUANTIFICATION Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2023-01-01 Hang Yang, Yuji Fujii, K. W. Wang, Alex A. Gorodetsky
We present a multifidelity uncertainty quantification numerical method that leverages the benefits of both sampling and surrogate modeling, while mitigating their downsides, for enabling rapid computation in complex dynamical systems such as automotive propulsion systems. In particular, the proposed method utilizes intrusive generalized polynomial chaos to quickly generate additional information that
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AdaAnn: ADAPTIVE ANNEALING SCHEDULER FOR PROBABILITY DENSITY APPROXIMATION Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2023-01-01 Emma R. Cobian, Jonathan D. Hauenstein, Fang Liu, Daniele E. Schiavazzi
Approximating probability distributions can be a challenging task, particularly when they are supported over regions of high geometrical complexity or exhibit multiple modes. Annealing can be used to facilitate this task which is often combined with constant a priori selected increments in inverse temperature. However, using constant increments limits the computational efficiency due to the inability
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AN ENHANCED FRAMEWORK FOR MORRIS BY COMBINING WITH A SEQUENTIAL SAMPLING STRATEGY Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2023-01-01 Qizhe Li, Hanyan Huang, Shan Xie, Lin Chen, Zecong Liu
The Morris method is an effective sample-based sensitivity analysis technique that has been applied in various disciplines. To ensure a more proper coverage of the input space and better performance, an enhanced framework for Morris is proposed by considering the combination of a sequential sampling strategy and the traditional Morris method. The paper introduces utilizing progressive Latin hypercube
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SHAPLEY EFFECT ESTIMATION IN RELIABILITY-ORIENTED SENSITIVITY ANALYSIS WITH CORRELATED INPUTS BY IMPORTANCE SAMPLING Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2023-01-01 Julien Demange-Chryst, François Bachoc, Jérôme Morio
Reliability-oriented sensitivity analysis aims at combining both reliability and sensitivity analyses by quantifying the influence of each input variable of a numerical model on a quantity of interest related to its failure. In particular, target sensitivity analysis focuses on the occurrence of the failure, and more precisely aims to determine which inputs are more likely to lead to the failure of
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BAYESIAN IDENTIFICATION OF PYROLYSIS MODEL PARAMETERS FOR THERMAL PROTECTION MATERIALS USING AN ADAPTIVE GRADIENT-INFORMED SAMPLING ALGORITHM WITH APPLICATION TO A MARS ATMOSPHERIC ENTRY Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2023-01-01 Joffrey Coheur, Thierry E. Magin, Philippe Chatelain, Maarten Arnst
For space missions involving atmospheric entry, a thermal protection system is essential to shield the spacecraft and its payload from the severe aerothermal loads. Carbon/phenolic composite materials have gained renewed interest to serve as ablative thermal protection materials (TPMs). New experimental data relevant to the pyrolytic decomposition of the phenolic resin used in such carbon/phenolic
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STOCHASTIC POLYNOMIAL CHAOS EXPANSIONS TO EMULATE STOCHASTIC SIMULATORS Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2023-01-01 Xujia Zhu, Bruno Sudret
In the context of uncertainty quantification, computational models are required to be repeatedly evaluated. This task is intractable for costly numerical models. Such a problem turns out to be even more severe for stochastic simulators, the output of which is a random variable for a given set of input parameters. To alleviate the computational burden, surrogate models are usually constructed and evaluated
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QUANTIFICATION AND PROPAGATION OF MODEL-FORM UNCERTAINTIES IN RANS TURBULENCE MODELING VIA INTRUSIVE POLYNOMIAL CHAOS Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2023-01-01 Jigar Parekh, R.W.C.P. Verstappen
Undeterred by its inherent limitations, Reynolds-averaged Navier-Stokes (RANS) based modeling is still considered the most recognized approach for several computational fluid dynamics (CFD) applications. Recently, in the turbulence modeling community, quantification of model-form uncertainties in RANS has attracted significant interest. We present a stochastic RANS solver with an efficient implementation
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GLOBAL SENSITIVITY ANALYSIS OF RARE EVENT PROBABILITIES USING SUBSET SIMULATION AND POLYNOMIAL CHAOS EXPANSIONS Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2023-01-01 Michael Merritt, Alen Alexanderian, Pierre A. Gremaud
By their very nature, rare event probabilities are expensive to compute; they are also delicate to estimate as their value strongly depends on distributional assumptions on the model parameters. Hence, understanding the sensitivity of the computed rare event probabilities to the hyper-parameters that define the distribution law of the model parameters is crucial. We show that by (i) accelerating the
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HAMILTONIAN MONTE CARLO IN INVERSE PROBLEMS. ILL-CONDITIONING AND MULTIMODALITY Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2023-01-01 Ian Langmore, M. Dikovsky, S. Geraedts, P. Norgaard, R. von Behren
The Hamiltonian Monte Carlo (HMC) method allows sampling from continuous densities. Favorable scaling with dimension has led to wide adoption of HMC by the statistics community. Modern autodifferentiating software should allow more widespread usage in Bayesian inverse problems. This paper analyzes two major difficulties encountered using HMC for inverse problems: poor conditioning and multimodality
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EFFICIENT APPROXIMATION OF HIGH-DIMENSIONAL EXPONENTIALS BY TENSOR NETWORKS Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2023-01-01 Martin Eigel, Nando Farchmin, Sebastian Heidenreich, P. Trunschke
In this work a general approach to compute a compressed representation of the exponential exp (h) of a high-dimensional function h is presented. Such exponential functions play an important role in several problems in uncertainty quantification, e.g., the approximation of log-normal random fields or the evaluation of Bayesian posterior measures. Usually, these high-dimensional objects are numerically
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MAXIMUM ENTROPY UNCERTAINTY MODELING AT THE FINITE ELEMENT LEVEL FOR HEATED STRUCTURES Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2023-01-01 P. Song, X. Q. Wang, Marc P. Mignolet
The focus of this paper is on the introduction of uncertainty on structural properties, including the thermal expansion coefficient, on linear finite element models of heated structures. A "mesoscale" approach is adopted here in which the uncertainty is introduced directly on the elemental matrices and vectors of each element by randomizing those corresponding to the mean model following the maximum
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CALCULATING PROBABILITY DENSITIES WITH HOMOTOPY, AND APPLICATIONS TO PARTICLE FILTERS Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2022-04-01 Juan Restrepo
We explore a homotopy sampling procedure and its generalization, loosely based on importance sampling, known as annealed importance sampling. The procedure makes use of a known probability distribution to find, via homotopy, the unknown normalization of a target distribution, as well as samples of the target distribution. In the context of stationary distributions that are associated with physical
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Learning high-dimensional probability distributions using tree tensor networks Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2022-04-01 Erwan Grelier, Anthony Nouy, Regis Lebrun
We consider the problem of the estimation of a high-dimensional probability distribution from i.i.d. samples of the distribution using model classes of functions in tree-based tensor formats, a particular case of tensor networks associated with a dimension partition tree. The distribution is assumed to admit a density with respect to a product measure, possibly discrete for handling the case of discrete
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Majorisation as a theory for uncertainty Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2022-03-01 Victoria Volodina, Nikki Sonenberg, Edward Wheatcroft, Henry Wynn
Majorisation, also called rearrangement inequalities, yields a type of stochastic ordering in which two or more distributions can be then compared. This method provides a representation of the peakedness of probability distributions and is also independent of the location of probabilities. These properties make majorisation a good candidate as a theory for uncertainty. We demonstrate that this approach
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A FULLY BAYESIAN GRADIENT-FREE SUPERVISED DIMENSION REDUCTION METHOD USING GAUSSIAN PROCESSES Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2022-01-01 Raphaël Gautier, Piyush Pandita, Sayan Ghosh, Dimitri Mavris
Modern day engineering problems are ubiquitously characterized by sophisticated computer codes that map parameters or inputs to an underlying physical process. In other situations, experimental setups are used to model the physical process in a laboratory, ensuring high precision while being costly in materials and logistics. In both scenarios, only a limited amount of data can be generated by querying
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EFFICIENT CALIBRATION FOR HIGH-DIMENSIONAL COMPUTER MODEL OUTPUT USING BASIS METHODS Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2022-01-01 James M. Salter, Daniel B. Williamson
Calibration of expensive computer models using emulators for high-dimensional output fields can become increasingly intractable with the size of the field(s) being compared to observational data. In these settings, dimension reduction is attractive, reducing the number of emulators required to mimic the field(s) by orders of magnitude. By comparing to popular independent emulation approaches that fit
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STOCHASTIC GALERKIN FINITE ELEMENT METHOD FOR NONLINEAR ELASTICITY AND APPLICATION TO REINFORCED CONCRETE MEMBERS Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2022-01-01 Mohammad S. Ghavami, Bedrich Sousedik, Hooshang Dabbagh, Morad Ahmadnasab
We develop a stochastic Galerkin finite element method for nonlinear elasticity and apply it to reinforced concrete members with random material properties. The strategy is based on the modified Newton-Raphson method, which consists of an incremental loading process and a linearization scheme applied at each load increment. We consider that the material properties are given by a stochastic expansion
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ADAPTIVE STRATIFIED SAMPLING FOR NONSMOOTH PROBLEMS Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2022-01-01 Per Pettersson, Sebastian Krumscheid
Science and engineering problems subject to uncertainty are frequently both computationally expensive and feature nonsmooth parameter dependence, making standard Monte Carlo too slow, and excluding efficient use of accelerated uncertainty quantification methods relying on strict smoothness assumptions. To remedy these challenges, we propose an adaptive stratification method suitable for nonsmooth problems
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METHOD FOR THE ANALYSIS OF EPISTEMIC AND ALEATORY UNCERTAINTIES FOR A RELIABLE EVALUATION OF FAILURE OF ENGINEERING STRUCTURES Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2022-01-01 Niklas Miska, Daniel Balzani
This contribution extends the known optimal uncertainty quantification (OUQ) framework to the capability of polymorphic uncertainty quantification by presenting two approaches to incorporate aleatory uncertainties, in addition to the epistemic uncertainties in the original framework. This enables the calculation of the sharpest bounds on the probability of failure of engineering structures given uncertain
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MANIFOLD LEARNING-BASED POLYNOMIAL CHAOS EXPANSIONS FOR HIGH-DIMENSIONAL SURROGATE MODELS Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2022-01-01 Katiana Kontolati, Dimitrios Loukrezis, Ketson R. M. dos Santos, Dimitrios G. Giovanis, Michael D. Shields
In this work we introduce a manifold learning-based method for uncertainty quantification (UQ) in systems describing complex spatiotemporal processes. Our first objective is to identify the embedding of a set of high-dimensional data representing quantities of interest of the computational or analytical model. For this purpose, we employ Grassmannian diffusion maps, a two-step nonlinear dimension reduction
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DYNAMICAL LOW-RANK APPROXIMATION FOR BURGERS' EQUATION WITH UNCERTAINTY Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2022-01-01 Jonas Kusch, Gianluca Ceruti, Lukas Einkemmer, Martin Frank
Quantifying uncertainties in hyperbolic equations is a source of several challenges. First, the solution forms shocks leading to oscillatory behavior in the numerical approximation of the solution. Second, the number of unknowns required for an effective discretization of the solution grows exponentially with the dimension of the uncertainties, yielding high computational costs and large memory requirements
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Lp CONVERGENCE OF APPROXIMATE MAPS AND PROBABILITY DENSITIES FOR FORWARD AND INVERSE PROBLEMS IN UNCERTAINTY QUANTIFICATION Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2022-01-01 Troy Butler, Timothy Wildey, W. Zhang
This work analyzes the convergence of probability densities solving uncertainty quantification problems for computational models where the mapping between input and output spaces is itself approximated. Specifically, we assume the exact mapping is replaced by a sequence of approximate maps that converges in Lp for some 1 ≤ p < ∞. To each approximate map, we then consider probability densities associated
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CONTROL VARIATES WITH A DIMENSION REDUCED BAYESIAN MONTE CARLO SAMPLER Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2022-01-01 Xin Cai, Junda Xiong, Hongqiao Wang, Jinglai Li
Evaluating the expectations of random functions is an important task in many fields of science and engineering. In practice, such an expectation is often evaluated with the Monte Carlo methods which rely on approximating the sought expectation with a sample average. It is well known that the Monte Carlo methods typically suffer from a slow convergence, which makes it especially undesirable for problems
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STABLE LIKELIHOOD COMPUTATION FOR MACHINE LEARNING OF LINEAR DIFFERENTIAL OPERATORS WITH GAUSSIAN PROCESSES Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2022-01-01 O. Chatrabgoun, Mohsen Esmaeilbeigi, M. Cheraghi, A. Daneshkhah
In many applied sciences, the main aim is to learn the parameters in the operational equations which best fit the observed data. A framework for solving such problems is to employ Gaussian process (GP) emulators which are well-known as nonparametric Bayesian machine learning techniques. GPs are among a class of methods known as kernel machines which can be used to approximate rather complex problems
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MULTILEVEL QUASI-MONTE CARLO FOR INTERVAL ANALYSIS Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2022-01-01 Robin R.P. Callens, Matthias G.R. Faess, David Moens
This paper presents a multilevel quasi-Monte Carlo method for interval analysis, as a computationally efficient method for high-dimensional linear models. Interval analysis typically requires a global optimization procedure to calculate the interval bounds on the output side of a computational model. The main issue of such a procedure is that it requires numerous full-scale model evaluations. Even
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MIXED COVARIANCE FUNCTION KRIGING MODEL FOR UNCERTAINTY QUANTIFICATION Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2022-01-01 Kai Cheng, Zhenzhou Lu, Sinan Xiao, Sergey Oladyshkin, Wolfgang Nowak
In this paper, we develop a mixed covariance function Kriging (MCF-Kriging) model for uncertainty quantification. The mixed covariance function is a linear combination of a traditional stationary covariance function and a nonsta-tionary covariance function constructed by the inner product of orthonormal polynomial basis functions. We use a weight matrix to control the contribution of each polynomial
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AUTOMATIC SELECTION OF BASIS-ADAPTIVE SPARSE POLYNOMIAL CHAOS EXPANSIONS FOR ENGINEERING APPLICATIONS Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2022-01-01 Nora Lüthen, Stefano Marelli, Bruno Sudret
Sparse polynomial chaos expansions (PCE) are an efficient and widely used surrogate modeling method in uncertainty quantification for engineering problems with computationally expensive models. To make use of the available information in the most efficient way, several approaches for so-called basis-adaptive sparse PCE have been proposed to determine the set of polynomial regressors ("basis") for PCE
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CLOSURE LAW MODEL UNCERTAINTY QUANTIFICATION Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2022-01-01 Andreas Strand, Jørn Kjølaas, Trond H. Bergstrøm, Ingelin Steinsland, Leif Rune Hellevik
The prediction uncertainty in simulators for industrial processes is due to uncertainties in the input variables and uncertainties in specification of the models, in particular the closure laws. In this work, the uncertainty in each closure law was modeled as a random variable and the parameters of its distribution were optimized to correctly quantify the uncertainty in predictions. We have developed
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SPARSE TENSOR PRODUCT APPROXIMATION FOR A CLASS OF GENERALIZED METHOD OF MOMENTS ESTIMATORS Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2022-01-01 Alexandros Gilch, Michael Griebel, Jens Oettershagen
Generalized method of moments (GMM) estimators in their various forms, including the popular maximum likelihood (ML) estimator, are frequently applied for the evaluation of complex econometric models without analytically computable moment or likelihood functions. As the objective functions of GMM- and ML-estimators themselves constitute the approximation of an integral, more precisely of the expected
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A FETI-DP-BASED PARALLEL ALGORITHM FOR SOLVING HIGH DIMENSIONAL STOCHASTIC PDES USING COLLOCATION Int. J. Uncertain. Quantif. (IF 1.7) Pub Date : 2022-01-01 Gopika Ajith, Debraj Ghosh
Numerical solution of stochastic partial differential equations often faces the challenge of large dimensionality due to discretization of the equation, random field coefficients, and the source term. Recently, domain decomposition (DD) methods have been successful in reducing the computational complexity and achieving parallelization for such problems. This improvement is due to reduction in the number