Relevant bibliographies by topics / Inverse Uncertainty Quantification

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
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Academic literature on the topic 'Inverse Uncertainty Quantification'

Author: Grafiati
Published: 25 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Inverse Uncertainty Quantification"

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Faes, Matthias, and David Moens. "Inverse Interval Field Quantification via Digital Image Correlation." Applied Mechanics and Materials 885 (November 2018): 304–10. http://dx.doi.org/10.4028/www.scientific.net/amm.885.304.

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This paper presents the application of a new method for the identification and quantification of interval valued spatial uncertainty under scarce data.Specifically, full-field strain measurements, obtained via Digital Image Correlation, are applied in conjunction with a quasi-static finite element model.To apply these high-dimensional but scarce data, extensions to the novel method are introduced.A case study, investigating spatial uncertainty in Young's modulus of PA-12 parts, produced via Laser Sintering, shows that an accurate quantification of the constituting uncertainty is possible, albeit being somewhat conservative with respect to deterministic values reported in literature.
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Talarico, Erick Costa e. Silva, Dario Grana, Leandro Passos de Figueiredo, and Sinesio Pesco. "Uncertainty quantification in seismic facies inversion." GEOPHYSICS 85, no. 4 (June 24, 2020): M43—M56. http://dx.doi.org/10.1190/geo2019-0392.1.

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In seismic reservoir characterization, facies prediction from seismic data often is formulated as an inverse problem. However, the uncertainty in the parameters that control their spatial distributions usually is not investigated. In a probabilistic setting, the vertical distribution of facies often is described by statistical models, such as Markov chains. Assuming that the transition probabilities in the vertical direction are known, the most likely facies sequence and its uncertainty can be obtained by computing the posterior distribution of a Bayesian inverse problem conditioned by seismic data. Generally, the model hyperparameters such as the transition matrix are inferred from seismic data and nearby wells using a Bayesian inference framework. It is assumed that there is a unique set of hyperparameters that optimally fit the measurements. The novelty of the proposed work is to investigate the nonuniqueness of the transition matrix and show the multimodality of their distribution. We then generalize the Bayesian inversion approach based on Markov chain models by assuming that the hyperparameters, the facies prior proportions and transition matrix, are unknown and derive the full posterior distribution. Including all of the possible transition matrices in the inversion improves the uncertainty quantification of the predicted facies conditioned by seismic data. Our method is demonstrated on synthetic and real seismic data sets, and it has high relevance in exploration studies due to the limited number of well data and in geologic environments with rapid lateral variations of the facies vertical distribution.
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Khuwaileh, B. A., and H. S. Abdel-Khalik. "Subspace-based Inverse Uncertainty Quantification for Nuclear Data Assessment." Nuclear Data Sheets 123 (January 2015): 57–61. http://dx.doi.org/10.1016/j.nds.2014.12.010.

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Tenorio, L., F. Andersson, M. de Hoop, and P. Ma. "Data analysis tools for uncertainty quantification of inverse problems." Inverse Problems 27, no. 4 (March 8, 2011): 045001. http://dx.doi.org/10.1088/0266-5611/27/4/045001.

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Sethurajan, Athinthra, Sergey Krachkovskiy, Gillian Goward, and Bartosz Protas. "Bayesian uncertainty quantification in inverse modeling of electrochemical systems." Journal of Computational Chemistry 40, no. 5 (December 28, 2018): 740–52. http://dx.doi.org/10.1002/jcc.25759.

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Hashemi, H., R. Berndtsson, M. Kompani-Zare, and M. Persson. "Natural vs. artificial groundwater recharge, quantification through inverse modeling." Hydrology and Earth System Sciences 17, no. 2 (February 11, 2013): 637–50. http://dx.doi.org/10.5194/hess-17-637-2013.

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Abstract. Estimating the change in groundwater recharge from an introduced artificial recharge system is important in order to evaluate future water availability. This paper presents an inverse modeling approach to quantify the recharge contribution from both an ephemeral river channel and an introduced artificial recharge system based on floodwater spreading in arid Iran. The study used the MODFLOW-2000 to estimate recharge for both steady- and unsteady-state conditions. The model was calibrated and verified based on the observed hydraulic head in observation wells and model precision, uncertainty, and model sensitivity were analyzed in all modeling steps. The results showed that in a normal year without extreme events, the floodwater spreading system is the main contributor to recharge with 80% and the ephemeral river channel with 20% of total recharge in the studied area. Uncertainty analysis revealed that the river channel recharge estimation represents relatively more uncertainty in comparison to the artificial recharge zones. The model is also less sensitive to the river channel. The results show that by expanding the artificial recharge system, the recharge volume can be increased even for small flood events, while the recharge through the river channel increases only for major flood events.
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Hashemi, H., R. Berndtsson, M. Kompani-Zare, and M. Persson. "Natural vs. artificial groundwater recharge, quantification through inverse modeling." Hydrology and Earth System Sciences Discussions 9, no. 8 (August 24, 2012): 9767–807. http://dx.doi.org/10.5194/hessd-9-9767-2012.

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Abstract. Estimating the change in groundwater recharge from an introduced artificial recharge system is important in order to evaluate future water availability. This paper presents an inverse modeling approach to quantify the recharge contribution from both an ephemeral river channel and an introduced artificial recharge system based on floodwater spreading in arid Iran. The study used the MODFLOW-2000 to estimate recharge for both steady and unsteady-state conditions. The model was calibrated and verified based on the observed hydraulic head in observation wells and model precision, uncertainty, and model sensitivity were analyzed in all modeling steps. The results showed that in a normal year without extreme events the floodwater spreading system is the main contributor to recharge with 80% and the ephemeral river channel with 20% of total recharge in the studied area. Uncertainty analysis revealed that the river channel recharge estimation represents relatively more uncertainty in comparison to the artificial recharge zones. The model is also less sensitive to the river channel. The results show that by expanding the artificial recharge system the recharge volume can be increased even for small flood events while the recharge through the river channel increases only for major flood events.
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Grana, Dario, Leandro Passos de Figueiredo, and Leonardo Azevedo. "Uncertainty quantification in Bayesian inverse problems with model and data dimension reduction." GEOPHYSICS 84, no. 6 (November 1, 2019): M15—M24. http://dx.doi.org/10.1190/geo2019-0222.1.

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The prediction of rock properties in the subsurface from geophysical data generally requires the solution of a mathematical inverse problem. Because of the large size of geophysical (seismic) data sets and subsurface models, it is common to reduce the dimension of the problem by applying dimension reduction methods and considering a reparameterization of the model and/or the data. Especially for high-dimensional nonlinear inverse problems, in which the analytical solution of the problem is not available in a closed form and iterative sampling or optimization methods must be applied to approximate the solution, model and/or data reduction reduce the computational cost of the inversion. However, part of the information in the data or in the model can be lost by working in the reduced model and/or data space. We have focused on the uncertainty quantification in the solution of the inverse problem with data and/or model order reduction. We operate in a Bayesian setting for the inversion and uncertainty quantification and validate the proposed approach in the linear case, in which the posterior distribution of the model variables can be analytically written and the uncertainty of the model predictions can be exactly assessed. To quantify the changes in the uncertainty in the inverse problem in the reduced space, we compare the uncertainty in the solution with and without data and/or model reduction. We then extend the approach to nonlinear inverse problems in which the solution is computed using an ensemble-based method. Examples of applications to linearized acoustic and nonlinear elastic inversion allow quantifying the impact of the application of reduction methods to model and data vectors on the uncertainty of inverse problem solutions. Examples of applications to linearized acoustic and nonlinear elastic inversion are shown.
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Dashti, M., and A. M. Stuart. "Uncertainty Quantification and Weak Approximation of an Elliptic Inverse Problem." SIAM Journal on Numerical Analysis 49, no. 6 (January 2011): 2524–42. http://dx.doi.org/10.1137/100814664.

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Acar, Pınar. "Uncertainty Quantification for Ti-7Al Alloy Microstructure with an Inverse Analytical Model (AUQLin)." Materials 12, no. 11 (May 31, 2019): 1773. http://dx.doi.org/10.3390/ma12111773.

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The present study addresses an inverse problem for observing the microstructural stochasticity given the variations in the macro-scale material properties by developing an analytical uncertainty quantification (UQ) model called AUQLin. The uncertainty in the material property is modeled with the analytical algorithm, and then the uncertainty propagation to the microstructure is solved with an inverse problem that utilizes the transformation of random variables principle. The inverse problem leads to an underdetermined linear system, and thus produces multiple solutions to the statistical features of the microstructure. The final solution is decided by solving an optimization problem which aims to minimize the difference between the computed and experimental statistical parameters of the microstructure. The final result for the computed microstructural uncertainty is found to provide a good match to the experimental microstructure information.
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Dissertations / Theses on the topic "Inverse Uncertainty Quantification"

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Chue, Bryan C. "Efficient Hessian computation in inverse problems with application to uncertainty quantification." Thesis, Boston University, 2013. https://hdl.handle.net/2144/21138.

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Thesis (M.Sc.Eng.) PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you.
This thesis considers the efficient Hessian computation in inverse problems with specific application to the elastography inverse problem. Inverse problems use measurements of observable parameters to infer information about model parameters, and tend to be ill-posed. They are typically formulated and solved as regularized constrained optimization problems, whose solutions best fit the measured data. Approaching the same inverse problem from a probabilistic Bayesian perspective produces the same optimal point called the maximum a posterior (MAP) estimate of the parameter distribution, but also produces a posterior probability distribution of the parameter estimate, from which a measure of the solution's uncertainty may be obtained. This probability distribution is a very high dimensional function with which it can be difficult to work. For example, in a modest application with N = 104 optimization variables, representing this function with just three values in each direction requires 3^10000 U+2248 10^5000 variables, which far exceeds the number of atoms in the universe. The uncertainty of the MAP estimate describes the shape of the probability distribution and to leading order may be parameterized by the covariance. Directly calculating the Hessian and hence the covariance, requires O(N) solutions of the constraint equations. Given the size of the problems of interest (N = O(10^4 - 10^6)), this is impractical. Instead, an accurate approximation of the Hessian can be assembled using a Krylov basis. The ill-posed nature of inverse problems suggests that its Hessian has low rank and therefore can be approximated with relatively few Krylov vectors. This thesis proposes a method to calculate this Krylov basis in the process of determining the MAP estimate of the parameter distribution. Using the Krylov space based conjugate gradient (CG) method, the MAP estimate is computed. Minor modifications to the algorithm permit storage of the Krylov approximation of the Hessian. As the accuracy of the Hessian approximation is directly related to the Krylov basis, long term orthogonality amongst the basis vectors is maintained via full reorthogonalization. Upon reaching the MAP estimate, the method produces a low rank approximation of the Hessian that can be used to compute the covariance.
2031-01-01
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Hebbur, Venkata Subba Rao Vishwas. "Adjoint based solution and uncertainty quantification techniques for variational inverse problems." Diss., Virginia Tech, 2015. http://hdl.handle.net/10919/76665.

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Variational inverse problems integrate computational simulations of physical phenomena with physical measurements in an informational feedback control system. Control parameters of the computational model are optimized such that the simulation results fit the physical measurements.The solution procedure is computationally expensive since it involves running the simulation computer model (the emph{forward model}) and the associated emph {adjoint model} multiple times. In practice, our knowledge of the underlying physics is incomplete and hence the associated computer model is laden with emph {model errors}. Similarly, it is not possible to measure the physical quantities exactly and hence the measurements are associated with emph {data errors}. The errors in data and model adversely affect the inference solutions. This work develops methods to address the challenges posed by the computational costs and by the impact of data and model errors in solving variational inverse problems. Variational inverse problems of interest here are formulated as optimization problems constrained by partial differential equations (PDEs). The solution process requires multiple evaluations of the constraints, therefore multiple solutions of the associated PDE. To alleviate the computational costs we develop a parallel in time discretization algorithm based on a nonlinear optimization approach. Like in the emph{parareal} approach, the time interval is partitioned into subintervals, and local time integrations are carried out in parallel. Solution continuity equations across interval boundaries are added as constraints. All the computational steps - forward solutions, gradients, and Hessian-vector products - involve only ideally parallel computations and therefore are highly scalable. This work develops a systematic mathematical framework to compute the impact of data and model errors on the solution to the variational inverse problems. The computational algorithm makes use of first and second order adjoints and provides an a-posteriori error estimate for a quantity of interest defined on the inverse solution (i.e., an aspect of the inverse solution). We illustrate the estimation algorithm on a shallow water model and on the Weather Research and Forecast model. Presence of outliers in measurement data is common, and this negatively impacts the solution to variational inverse problems. The traditional approach, where the inverse problem is formulated as a minimization problem in $L_2$ norm, is especially sensitive to large data errors. To alleviate the impact of data outliers we propose to use robust norms such as the $L_1$ and Huber norm in data assimilation. This work develops a systematic mathematical framework to perform three and four dimensional variational data assimilation using $L_1$ and Huber norms. The power of this approach is demonstrated by solving data assimilation problems where measurements contain outliers.
Ph. D.
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Devathi, Duttaabhinivesh. "Uncertainty Quantification for Underdetermined Inverse Problems via Krylov Subspace Iterative Solvers." Case Western Reserve University School of Graduate Studies / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=case155446130705089.

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Andersson, Hjalmar. "Inverse Uncertainty Quantification using deterministic sampling : An intercomparison between different IUQ methods." Thesis, Uppsala universitet, Tillämpad kärnfysik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-447070.

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In this thesis, two novel methods for Inverse Uncertainty Quantification are benchmarked against the more established methods of Monte Carlo sampling of output parameters(MC) and Maximum Likelihood Estimation (MLE). Inverse Uncertainty Quantification (IUQ) is the process of how to best estimate the values of the input parameters in a simulation, and the uncertainty of said estimation, given a measurement of the output parameters. The two new methods are Deterministic Sampling (DS) and Weight Fixing (WF). Deterministic sampling uses a set of sampled points such that the set of points has the same statistic as the output. For each point, the corresponding point of the input is found to be able to calculate the statistics of the input. Weight fixing uses random samples from the rough region around the input to create a linear problem that involves finding the right weights so that the output has the right statistic. The benchmarking between the four methods shows that both DS and WF are comparably accurate to both MC and MLE in most cases tested in this thesis. It was also found that both DS and WF uses approximately the same amount of function calls as MLE and all three methods use a lot fewer function calls to the simulation than MC. It was discovered that WF is not always able to find a solution. This is probably because the methods used for WF are not the optimal method for what they are supposed to do. Finding more optimal methods for WF is something that could be investigated further.
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Lal, Rajnesh. "Data assimilation and uncertainty quantification in cardiovascular biomechanics." Thesis, Montpellier, 2017. http://www.theses.fr/2017MONTS088/document.

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Les simulations numériques des écoulements sanguins cardiovasculaires peuvent combler d’importantes lacunes dans les capacités actuelles de traitement clinique. En effet, elles offrent des moyens non invasifs pour quantifier l’hémodynamique dans le cœur et les principaux vaisseaux sanguins chez les patients atteints de maladies cardiovasculaires. Ainsi, elles permettent de recouvrer les caractéristiques des écoulements sanguins qui ne peuvent pas être obtenues directement à partir de l’imagerie médicale. Dans ce sens, des simulations personnalisées utilisant des informations propres aux patients aideraient à une prévision individualisée des risques. Nous pourrions en effet, disposer des informations clés sur la progression éventuelle d’une maladie ou détecter de possibles anomalies physiologiques. Les modèles numériques peuvent fournir également des moyens pour concevoir et tester de nouveaux dispositifs médicaux et peuvent être utilisés comme outils prédictifs pour la planification de traitement chirurgical personnalisé. Ils aideront ainsi à la prise de décision clinique. Cependant, une difficulté dans cette approche est que, pour être fiables, les simulations prédictives spécifiques aux patients nécessitent une assimilation efficace de leurs données médicales. Ceci nécessite la solution d’un problème hémodynamique inverse, où les paramètres du modèle sont incertains et sont estimés à l’aide des techniques d’assimilation de données.Dans cette thèse, le problème inverse pour l’estimation des paramètres est résolu par une méthode d’assimilation de données basée sur un filtre de Kalman d’ensemble (EnKF). Connaissant les incertitudes sur les mesures, un tel filtre permet la quantification des incertitudes liées aux paramètres estimés. Un algorithme d’estimation de paramètres, basé sur un filtre de Kalman d’ensemble, est proposé dans cette thèse pour des calculs hémodynamiques spécifiques à un patient, dans un réseau artériel schématique et à partir de mesures cliniques incertaines. La méthodologie est validée à travers plusieurs scenarii in silico utilisant des données synthétiques. La performance de l’algorithme d’estimation de paramètres est également évaluée sur des données expérimentales pour plusieurs réseaux artériels et dans un cas provenant d’un banc d’essai in vitro et des données cliniques réelles d’un volontaire (cas spécifique du patient). Le but principal de cette thèse est l’analyse hémodynamique spécifique du patient dans le polygone de Willis, appelé aussi cercle artériel du cerveau. Les propriétés hémodynamiques communes, comme celles de la paroi artérielle (module de Young, épaisseur de la paroi et coefficient viscoélastique), et les paramètres des conditions aux limites (coefficients de réflexion et paramètres du modèle de Windkessel) sont estimés. Il est également démontré qu’un modèle appelé compartiment d’ordre réduit (ou modèle dimension zéro) permet une estimation simple et fiable des caractéristiques du flux sanguin dans le polygone de Willis. De plus, il est ressorti que les simulations avec les paramètres estimés capturent les formes attendues pour les ondes de pression et de débit aux emplacements prescrits par le clinicien
Cardiovascular blood flow simulations can fill several critical gaps in current clinical capabilities. They offer non-invasive ways to quantify hemodynamics in the heart and major blood vessels for patients with cardiovascular diseases, that cannot be directly obtained from medical imaging. Patient-specific simulations (incorporating data unique to the individual) enable individualised risk prediction, provide key insights into disease progression and/or abnormal physiologic detection. They also provide means to systematically design and test new medical devices, and are used as predictive tools to surgical and personalize treatment planning and, thus aid in clinical decision-making. Patient-specific predictive simulations require effective assimilation of medical data for reliable simulated predictions. This is usually achieved by the solution of an inverse hemodynamic problem, where uncertain model parameters are estimated using the techniques for merging data and numerical models known as data assimilation methods.In this thesis, the inverse problem is solved through a data assimilation method using an ensemble Kalman filter (EnKF) for parameter estimation. By using an ensemble Kalman filter, the solution also comes with a quantification of the uncertainties for the estimated parameters. An ensemble Kalman filter-based parameter estimation algorithm is proposed for patient-specific hemodynamic computations in a schematic arterial network from uncertain clinical measurements. Several in silico scenarii (using synthetic data) are considered to investigate the efficiency of the parameter estimation algorithm using EnKF. The usefulness of the parameter estimation algorithm is also assessed using experimental data from an in vitro test rig and actual real clinical data from a volunteer (patient-specific case). The proposed algorithm is evaluated on arterial networks which include single arteries, cases of bifurcation, a simple human arterial network and a complex arterial network including the circle of Willis.The ultimate aim is to perform patient-specific hemodynamic analysis in the network of the circle of Willis. Common hemodynamic properties (parameters), like arterial wall properties (Young’s modulus, wall thickness, and viscoelastic coefficient) and terminal boundary parameters (reflection coefficient and Windkessel model parameters) are estimated as the solution to an inverse problem using time series pressure values and blood flow rate as measurements. It is also demonstrated that a proper reduced order zero-dimensional compartment model can lead to a simple and reliable estimation of blood flow features in the circle of Willis. The simulations with the estimated parameters capture target pressure or flow rate waveforms at given specific locations
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Narayanamurthi, Mahesh. "Advanced Time Integration Methods with Applications to Simulation, Inverse Problems, and Uncertainty Quantification." Diss., Virginia Tech, 2020. http://hdl.handle.net/10919/104357.

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Simulation and optimization of complex physical systems are an integral part of modern science and engineering. The systems of interest in many fields have a multiphysics nature, with complex interactions between physical, chemical and in some cases even biological processes. This dissertation seeks to advance forward and adjoint numerical time integration methodologies for the simulation and optimization of semi-discretized multiphysics partial differential equations (PDEs), and to estimate and control numerical errors via a goal-oriented a posteriori error framework. We extend exponential propagation iterative methods of Runge-Kutta type (EPIRK) by [Tokman, JCP 2011], to build EPIRK-W and EPIRK-K time integration methods that admit approximate Jacobians in the matrix-exponential like operations. EPIRK-W methods extend the W-method theory by [Steihaug and Wofbrandt, Math. Comp. 1979] to preserve their order of accuracy under arbitrary Jacobian approximations. EPIRK-K methods extend the theory of K-methods by [Tranquilli and Sandu, JCP 2014] to EPIRK and use a Krylov-subspace based approximation of Jacobians to gain computational efficiency. New families of partitioned exponential methods for multiphysics problems are developed using the classical order condition theory via particular variants of T-trees and corresponding B-series. The new partitioned methods are found to perform better than traditional unpartitioned exponential methods for some problems in mild-medium stiffness regimes. Subsequently, partitioned stiff exponential Runge-Kutta (PEXPRK) methods -- that extend stiffly accurate exponential Runge-Kutta methods from [Hochbruck and Ostermann, SINUM 2005] to a multiphysics context -- are constructed and analyzed. PEXPRK methods show full convergence under various splittings of a diffusion-reaction system. We address the problem of estimation of numerical errors in a multiphysics discretization by developing a goal-oriented a posteriori error framework. Discrete adjoints of GARK methods are derived from their forward formulation [Sandu and Guenther, SINUM 2015]. Based on these, we build a posteriori estimators for both spatial and temporal discretization errors. We validate the estimators on a number of reaction-diffusion systems and use it to simultaneously refine spatial and temporal grids.
Doctor of Philosophy
The study of modern science and engineering begins with descriptions of a system of mathematical equations (a model). Different models require different techniques to both accurately and effectively solve them on a computer. In this dissertation, we focus on developing novel mathematical solvers for models expressed as a system of equations, where only the initial state and the rate of change of state as a function are known. The solvers we develop can be used to both forecast the behavior of the system and to optimize its characteristics to achieve specific goals. We also build methodologies to estimate and control errors introduced by mathematical solvers in obtaining a solution for models involving multiple interacting physical, chemical, or biological phenomena. Our solvers build on state of the art in the research community by introducing new approximations that exploit the underlying mathematical structure of a model. Where it is necessary, we provide concrete mathematical proofs to validate theoretically the correctness of the approximations we introduce and correlate with follow-up experiments. We also present detailed descriptions of the procedure for implementing each mathematical solver that we develop throughout the dissertation while emphasizing on means to obtain maximal performance from the solver. We demonstrate significant performance improvements on a range of models that serve as running examples, describing chemical reactions among distinct species as they diffuse over a surface medium. Also provided are results and procedures that a curious researcher can use to advance the ideas presented in the dissertation to other types of solvers that we have not considered. Research on mathematical solvers for different mathematical models is rich and rewarding with numerous open-ended questions and is a critical component in the progress of modern science and engineering.
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Ray, Kolyan Michael. "Asymptotic theory for Bayesian nonparametric procedures in inverse problems." Thesis, University of Cambridge, 2015. https://www.repository.cam.ac.uk/handle/1810/278387.

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The main goal of this thesis is to investigate the frequentist asymptotic properties of nonparametric Bayesian procedures in inverse problems and the Gaussian white noise model. In the first part, we study the frequentist posterior contraction rate of nonparametric Bayesian procedures in linear inverse problems in both the mildly and severely ill-posed cases. This rate provides a quantitative measure of the quality of statistical estimation of the procedure. A theorem is proved in a general Hilbert space setting under approximation-theoretic assumptions on the prior. The result is applied to non-conjugate priors, notably sieve and wavelet series priors, as well as in the conjugate setting. In the mildly ill-posed setting, minimax optimal rates are obtained, with sieve priors being rate adaptive over Sobolev classes. In the severely ill-posed setting, oversmoothing the prior yields minimax rates. Previously established results in the conjugate setting are obtained using this method. Examples of applications include deconvolution, recovering the initial condition in the heat equation and the Radon transform. In the second part of this thesis, we investigate Bernstein--von Mises type results for adaptive nonparametric Bayesian procedures in both the Gaussian white noise model and the mildly ill-posed inverse setting. The Bernstein--von Mises theorem details the asymptotic behaviour of the posterior distribution and provides a frequentist justification for the Bayesian approach to uncertainty quantification. We establish weak Bernstein--von Mises theorems in both a Hilbert space and multiscale setting, which have applications in $L^2$ and $L^\infty$ respectively. This provides a theoretical justification for plug-in procedures, for example the use of certain credible sets for sufficiently smooth linear functionals. We use this general approach to construct optimal frequentist confidence sets using a Bayesian approach. We also provide simulations to numerically illustrate our approach and obtain a visual representation of the different geometries involved.
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Alhossen, Iman. "Méthode d'analyse de sensibilité et propagation inverse d'incertitude appliquées sur les modèles mathématiques dans les applications d'ingénierie." Thesis, Toulouse 3, 2017. http://www.theses.fr/2017TOU30314/document.

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Dans de nombreuses disciplines, les approches permettant d'étudier et de quantifier l'influence de données incertaines sont devenues une nécessité. Bien que la propagation directe d'incertitudes ait été largement étudiée, la propagation inverse d'incertitudes demeure un vaste sujet d'étude, sans méthode standardisée. Dans cette thèse, une nouvelle méthode de propagation inverse d'incertitude est présentée. Le but de cette méthode est de déterminer l'incertitude d'entrée à partir de données de sortie considérées comme incertaines. Parallèlement, les méthodes d'analyse de sensibilité sont également très utilisées pour déterminer l'influence des entrées sur la sortie lors d'un processus de modélisation. Ces approches permettent d'isoler les entrées les plus significatives, c'est à dire les plus influentes, qu'il est nécessaire de tester lors d'une analyse d'incertitudes. Dans ce travail, nous approfondirons tout d'abord la méthode d'analyse de sensibilité de Sobol, qui est l'une des méthodes d'analyse de sensibilité globale les plus efficaces. Cette méthode repose sur le calcul d'indices de sensibilité, appelés indices de Sobol, qui représentent l'effet des données d'entrées (vues comme des variables aléatoires continues) sur la sortie. Nous démontrerons ensuite que la méthode de Sobol donne des résultats fiables même lorsqu'elle est appliquée dans le cas discret. Puis, nous étendrons le cadre d'application de la méthode de Sobol afin de répondre à la problématique de propagation inverse d'incertitudes. Enfin, nous proposerons une nouvelle approche de la méthode de Sobol qui permet d'étudier la variation des indices de sensibilité par rapport à certains facteurs du modèle ou à certaines conditions expérimentales. Nous montrerons que les résultats obtenus lors de ces études permettent d'illustrer les différentes caractéristiques des données d'entrée. Pour conclure, nous exposerons comment ces résultats permettent d'indiquer les meilleures conditions expérimentales pour lesquelles l'estimation des paramètres peut être efficacement réalisée
Approaches for studying uncertainty are of great necessity in all disciplines. While the forward propagation of uncertainty has been investigated extensively, the backward propagation is still under studied. In this thesis, a new method for backward propagation of uncertainty is presented. The aim of this method is to determine the input uncertainty starting from the given data of the uncertain output. In parallel, sensitivity analysis methods are also of great necessity in revealing the influence of the inputs on the output in any modeling process. This helps in revealing the most significant inputs to be carried in an uncertainty study. In this work, the Sobol sensitivity analysis method, which is one of the most efficient global sensitivity analysis methods, is considered and its application framework is developed. This method relies on the computation of sensitivity indexes, called Sobol indexes. These indexes give the effect of the inputs on the output. Usually inputs in Sobol method are considered to vary as continuous random variables in order to compute the corresponding indexes. In this work, the Sobol method is demonstrated to give reliable results even when applied in the discrete case. In addition, another advancement for the application of the Sobol method is done by studying the variation of these indexes with respect to some factors of the model or some experimental conditions. The consequences and conclusions derived from the study of this variation help in determining different characteristics and information about the inputs. Moreover, these inferences allow the indication of the best experimental conditions at which estimation of the inputs can be done
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9

Gehre, Matthias [Verfasser], Peter [Akademischer Betreuer] Maaß, and Bangti [Akademischer Betreuer] Jin. "Rapid Uncertainty Quantification for Nonlinear Inverse Problems / Matthias Gehre. Gutachter: Peter Maaß ; Bangti Jin. Betreuer: Peter Maaß." Bremen : Staats- und Universitätsbibliothek Bremen, 2013. http://d-nb.info/1072078589/34.

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10

Kamilis, Dimitrios. "Uncertainty Quantification for low-frequency Maxwell equations with stochastic conductivity models." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/31415.

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Abstract:
Uncertainty Quantification (UQ) has been an active area of research in recent years with a wide range of applications in data and imaging sciences. In many problems, the source of uncertainty stems from an unknown parameter in the model. In physical and engineering systems for example, the parameters of the partial differential equation (PDE) that model the observed data may be unknown or incompletely specified. In such cases, one may use a probabilistic description based on prior information and formulate a forward UQ problem of characterising the uncertainty in the PDE solution and observations in response to that in the parameters. Conversely, inverse UQ encompasses the statistical estimation of the unknown parameters from the available observations, which can be cast as a Bayesian inverse problem. The contributions of the thesis focus on examining the aforementioned forward and inverse UQ problems for the low-frequency, time-harmonic Maxwell equations, where the model uncertainty emanates from the lack of knowledge of the material conductivity parameter. The motivation comes from the Controlled-Source Electromagnetic Method (CSEM) that aims to detect and image hydrocarbon reservoirs by using electromagnetic field (EM) measurements to obtain information about the conductivity profile of the sub-seabed. Traditionally, algorithms for deterministic models have been employed to solve the inverse problem in CSEM by optimisation and regularisation methods, which aside from the image reconstruction provide no quantitative information on the credibility of its features. This work employs instead stochastic models where the conductivity is represented as a lognormal random field, with the objective of providing a more informative characterisation of the model observables and the unknown parameters. The variational formulation of these stochastic models is analysed and proved to be well-posed under suitable assumptions. For computational purposes the stochastic formulation is recast as a deterministic, parametric problem with distributed uncertainty, which leads to an infinite-dimensional integration problem with respect to the prior and posterior measure. One of the main challenges is thus the approximation of these integrals, with the standard choice being some variant of the Monte-Carlo (MC) method. However, such methods typically fail to take advantage of the intrinsic properties of the model and suffer from unsatisfactory convergence rates. Based on recently developed theory on high-dimensional approximation, this thesis advocates the use of Sparse Quadrature (SQ) to tackle the integration problem. For the models considered here and under certain assumptions, we prove that for forward UQ, Sparse Quadrature can attain dimension-independent convergence rates that out-perform MC. Typical CSEM models are large-scale and thus additional effort is made in this work to reduce the cost of obtaining forward solutions for each sampling parameter by utilising the weighted Reduced Basis method (RB) and the Empirical Interpolation Method (EIM). The proposed variant of a combined SQ-EIM-RB algorithm is based on an adaptive selection of training sets and a primal-dual, goal-oriented formulation for the EIM-RB approximation. Numerical examples show that the suggested computational framework can alleviate the computational costs associated with forward UQ for the pertinent large-scale models, thus providing a viable methodology for practical applications.
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Books on the topic "Inverse Uncertainty Quantification"

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Large-scale inverse problems and quantification of uncertainty. Hoboken, N.J: Wiley, 2010.

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Biegler, Lorenz, George Biros, Omar Ghattas, Matthias Heinkenschloss, and Bani Mallick. Large-Scale Inverse Problems and Quantification of Uncertainty. Wiley & Sons, Incorporated, John, 2010.

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Biegler, Lorenz, George Biros, Omar Ghattas, Matthias Heinkenschloss, and Bani Mallick. Large-Scale Inverse Problems and Quantification of Uncertainty. Wiley & Sons, Incorporated, John, 2011.

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Biegler, Lorenz, George Biros, Omar Ghattas, Matthias Heinkenschloss, and Bani Mallick. Large-Scale Inverse Problems and Quantification of Uncertainty. Wiley & Sons, Incorporated, John, 2011.

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Biegler, Lorenz, George Biros, Omar Ghattas, Matthias Heinkenschloss, David Keyes, Bani Mallick, Youssef Marzouk, Luis Tenorio, Bart van Bloemen Waanders, and Karen Willcox, eds. Large‐Scale Inverse Problems and Quantification of Uncertainty. Wiley, 2010. http://dx.doi.org/10.1002/9780470685853.

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Book chapters on the topic "Inverse Uncertainty Quantification"

1

Soize, Christian. "Fundamental Tools for Statistical Inverse Problems." In Uncertainty Quantification, 141–53. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-54339-0_7.

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Dashti, Masoumeh, and Andrew M. Stuart. "The Bayesian Approach to Inverse Problems." In Handbook of Uncertainty Quantification, 311–428. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-12385-1_7.

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Dashti, Masoumeh, and Andrew M. Stuart. "The Bayesian Approach to Inverse Problems." In Handbook of Uncertainty Quantification, 1–118. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-11259-6_7-1.

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Soize, Christian. "Random Vectors and Random Fields in High Dimension: Parametric Model-Based Representation, Identification from Data, and Inverse Problems." In Handbook of Uncertainty Quantification, 883–935. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-12385-1_30.

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Soize, Christian. "Random Vectors and Random Fields in High Dimension: Parametric Model-Based Representation, Identification from Data, and Inverse Problems." In Handbook of Uncertainty Quantification, 1–53. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-11259-6_30-1.

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Kitanidis, P. K. "Bayesian and Geostatistical Approaches to Inverse Problems." In Large-Scale Inverse Problems and Quantification of Uncertainty, 71–85. Chichester, UK: John Wiley & Sons, Ltd, 2010. http://dx.doi.org/10.1002/9780470685853.ch4.

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Sandu, A. "Solution of Inverse Problems using Discrete ODE Adjoints." In Large-Scale Inverse Problems and Quantification of Uncertainty, 345–65. Chichester, UK: John Wiley & Sons, Ltd, 2010. http://dx.doi.org/10.1002/9780470685853.ch16.

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Qiao, Baijie, Zhu Mao, Jinxin Liu, and Xuefeng Chen. "Sparse Deconvolution for the Inverse Problem of Multiple-Impact Force Identification." In Model Validation and Uncertainty Quantification, Volume 3, 1–9. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-74793-4_1.

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Delbos, F., C. Duffet, and D. Sinoquet. "Uncertainty Analysis for Seismic Inverse Problems: Two Practical Examples." In Large-Scale Inverse Problems and Quantification of Uncertainty, 321–43. Chichester, UK: John Wiley & Sons, Ltd, 2010. http://dx.doi.org/10.1002/9780470685853.ch15.

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Zabaras, N. "Solving Stochastic Inverse Problems: A Sparse Grid Collocation Approach." In Large-Scale Inverse Problems and Quantification of Uncertainty, 291–319. Chichester, UK: John Wiley & Sons, Ltd, 2010. http://dx.doi.org/10.1002/9780470685853.ch14.

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Conference papers on the topic "Inverse Uncertainty Quantification"

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Friswell, Michael, Jose Fonseca, John Mottershead, and Arthur Lees. "Quantification of Uncertainty Using Inverse Methods." In 45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2004. http://dx.doi.org/10.2514/6.2004-1672.

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Houpert, Corentin, Josselin Garnier, and Philippe Humbert. "INVERSE PROBLEMS FOR STOCHASTIC NEUTRONICS." In 4th International Conference on Uncertainty Quantification in Computational Sciences and Engineering. Athens: Institute of Research and Development for Computational Methods in Engineering Sciences (ICMES), 2021. http://dx.doi.org/10.7712/120221.8022.18997.

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Tsilifis, Panagiotis, Ilias Bilionis, Ioannis Katsounaros, and Nicholas Zabaras. "VARIATIONAL REFORMULATION OF BAYESIAN INVERSE PROBLEMS." In 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering. Athens: Institute of Structural Analysis and Antiseismic Research School of Civil Engineering National Technical University of Athens (NTUA) Greece, 2015. http://dx.doi.org/10.7712/120215.4308.529.

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de Figueiredo, Leandro, Dario Grana, Leonardo Azevedo, Mauro Roisenberg, and Bruno Rodrigues. "Uncertainty quantification in linear inverse problems with dimension reduction." In International Congress of the Brazilian Geophysical Society&Expogef. Brazilian Geophysical Society, 2019. http://dx.doi.org/10.22564/16cisbgf2019.110.

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Soize, C., C. Desceliers, J. Guilleminot, T. T. Le, M. T. Nguyen, G. Perrin, J. M. Allain, H. Gharbi, D. Duhamel, and C. Funfschilling. "STOCHASTIC REPRESENTATIONS AND STATISTICAL INVERSE IDENTIFICATION FOR UNCERTAINTY QUANTIFICATION IN COMPUTATIONAL MECHANICS." In 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering. Athens: Institute of Structural Analysis and Antiseismic Research School of Civil Engineering National Technical University of Athens (NTUA) Greece, 2015. http://dx.doi.org/10.7712/120215.4249.527.

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Bogaerts, Lars, Matthias Faes, and David Moens. "A MACHINE LEARNING APPROACH FOR THE INVERSE QUANTIFICATION OF SET-THEORETICAL UNCERTAINTY." In 2nd International Conference on Uncertainty Quantification in Computational Sciences and Engineering. Athens: Institute of Structural Analysis and Antiseismic Research School of Civil Engineering National Technical University of Athens (NTUA) Greece, 2019. http://dx.doi.org/10.7712/120219.6334.18848.

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Mackie, Randall L., Federico Miorelli, and Max A. Meju. "Practical methods for model uncertainty quantification in electromagnetic inverse problems." In SEG Technical Program Expanded Abstracts 2018. Society of Exploration Geophysicists, 2018. http://dx.doi.org/10.1190/segam2018-2997269.1.

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Mackie, R., M. Meju, and F. Miorelli. "Practical Methods For Model Uncertainty Quantification In Geophysical Inverse Problems." In EAGE Conference on Reservoir Geoscience. European Association of Geoscientists & Engineers, 2018. http://dx.doi.org/10.3997/2214-4609.201803267.

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Perrin, G., and C. Soize. "STATISTICAL INVERSE PROBLEMS FOR NON-GAUSSIAN NON-STATIONARY STOCHASTIC PROCESSES DEFINED BY A SET OF REALIZATIONS." In 1st International Conference on Uncertainty Quantification in Computational Sciences and Engineering. Athens: Institute of Structural Analysis and Antiseismic Research School of Civil Engineering National Technical University of Athens (NTUA) Greece, 2015. http://dx.doi.org/10.7712/120215.4259.856.

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Ranjan, Reetesh, Shubham Karpe, Pavan Patel, and Suresh Menon. "Assessment of Surrogate Models for Inverse Uncertainty Quantification of Simulant Combustion." In AIAA Scitech 2020 Forum. Reston, Virginia: American Institute of Aeronautics and Astronautics, 2020. http://dx.doi.org/10.2514/6.2020-2137.

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Reports on the topic "Inverse Uncertainty Quantification"

1

Fowler, Michael James. Generalized Uncertainty Quantification for Linear Inverse Problems in X-ray Imaging. Office of Scientific and Technical Information (OSTI), April 2014. http://dx.doi.org/10.2172/1179471.

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Favorite, Jeffrey A., Garrett James Dean, Keith C. Bledsoe, Matt Jessee, Dan Gabriel Cacuci, Ruixian Fang, and Madalina Badea. Predictive Modeling, Inverse Problems, and Uncertainty Quantification with Application to Emergency Response. Office of Scientific and Technical Information (OSTI), April 2018. http://dx.doi.org/10.2172/1432629.

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Biros, George. Uncertainity Quantification for Large Scale Inverse Scattering. Fort Belvoir, VA: Defense Technical Information Center, April 2013. http://dx.doi.org/10.21236/ada578547.

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