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Journal articles on the topic 'Inverse Uncertainty Quantification'

Author: Grafiati

Published: 25 June 2021

Last updated: 1 February 2022

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1

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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2

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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4

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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6

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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9

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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10

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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11

Honjo, Yusuke, and Thuraisamy Thavaraj. "On uncertainty evaluation of contaminant migration through clayey barriers." Canadian Geotechnical Journal 31, no. 5 (October 1, 1994): 637–48. http://dx.doi.org/10.1139/t94-076.

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This paper presents a methodology to estimate parameters and to make predictions with quantified uncertainty for an advective–diffusive transport of nonreactive species and low-concentration reactive species through saturated porous media. The methodology is put in the framework of inverse and forward analyses. The maximum-likelihood method (or the weighted least square method) is employed in the inverse analysis, whereas the first-order second-moment method is used in the forward analysis. The methodology facilitates the quantification of uncertainty in the estimated parameters as well as in the predictions. A case study consisting of sets of laboratory tests and field data taken from the literature is used to demonstrate the capability of the proposed methodologies. It is generally recognized that the advective–diffusive transport of contaminants is a rather uncertain process in prediction; therefore the methodology proposed in this study should be useful for practising geotechnical engineers. Key words : statistical analysis, contaminant migration, diffusion, clay barrier, inverse analysis, waste disposal.

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12

Nagel, Joseph B., and Bruno Sudret. "A unified framework for multilevel uncertainty quantification in Bayesian inverse problems." Probabilistic Engineering Mechanics 43 (January 2016): 68–84. http://dx.doi.org/10.1016/j.probengmech.2015.09.007.

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13

Klein, Olaf, Daniele Davino, and Ciro Visone. "On forward and inverse uncertainty quantification for models involving hysteresis operators." Mathematical Modelling of Natural Phenomena 15 (2020): 53. http://dx.doi.org/10.1051/mmnp/2020009.

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Parameters within hysteresis operators modeling real world objects have to be identified from measurements and are therefore subject to corresponding errors. To investigate the influence of these errors, the methods of Uncertainty Quantification (UQ) are applied. Results of forward UQ for a play operator with a stochastic yield limit are presented. Moreover, inverse UQ is performed to identify the parameters in the weight function in a Prandtl-Ishlinskiĭ operator and the uncertainties of these parameters.

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14

Bardsley, Johnathan M., and Colin Fox. "An MCMC method for uncertainty quantification in nonnegativity constrained inverse problems." Inverse Problems in Science and Engineering 20, no. 4 (June 2012): 477–98. http://dx.doi.org/10.1080/17415977.2011.637208.

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Malinverno, Alberto, and Victoria A. Briggs. "Expanded uncertainty quantification in inverse problems: Hierarchical Bayes and empirical Bayes." GEOPHYSICS 69, no. 4 (July 2004): 1005–16. http://dx.doi.org/10.1190/1.1778243.

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A common way to account for uncertainty in inverse problems is to apply Bayes' rule and obtain a posterior distribution of the quantities of interest given a set of measurements. A conventional Bayesian treatment, however, requires assuming specific values for parameters of the prior distribution and of the distribution of the measurement errors (e.g., the standard deviation of the errors). In practice, these parameters are often poorly known a priori, and choosing a particular value is often problematic. Moreover, the posterior uncertainty is computed assuming that these parameters are fixed; if they are not well known a priori, the posterior uncertainties have dubious value. This paper describes extensions to the conventional Bayesian treatment that assign uncertainty to the parameters defining the prior distribution and the distribution of the measurement errors. These extensions are known in the statistical literature as “empirical Bayes” and “hierarchical Bayes.” We demonstrate the practical application of these approaches to a simple linear inverse problem: using seismic traveltimes measured by a receiver in a well to infer compressional wave slowness in a 1D earth model. These procedures do not require choosing fixed values for poorly known parameters and, at most, need a realistic range (e.g., a minimum and maximum value for the standard deviation of the measurement errors). Inversion is thus made easier for general users, who are not required to set parameters they know little about.

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Yang, Xiu, Weixuan Li, and Alexandre Tartakovsky. "Sliced-Inverse-Regression--Aided Rotated Compressive Sensing Method for Uncertainty Quantification." SIAM/ASA Journal on Uncertainty Quantification 6, no. 4 (January 2018): 1532–54. http://dx.doi.org/10.1137/17m1148955.

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Repetti, Audrey, Marcelo Pereyra, and Yves Wiaux. "Scalable Bayesian Uncertainty Quantification in Imaging Inverse Problems via Convex Optimization." SIAM Journal on Imaging Sciences 12, no. 1 (January 2019): 87–118. http://dx.doi.org/10.1137/18m1173629.

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18

Giordano, Matteo, and Hanne Kekkonen. "Bernstein--von Mises Theorems and Uncertainty Quantification for Linear Inverse Problems." SIAM/ASA Journal on Uncertainty Quantification 8, no. 1 (January 2020): 342–73. http://dx.doi.org/10.1137/18m1226269.

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19

Fang, Zhilong, Curt Da Silva, Rachel Kuske, and Felix J. Herrmann. "Uncertainty quantification for inverse problems with weak partial-differential-equation constraints." GEOPHYSICS 83, no. 6 (November 1, 2018): R629—R647. http://dx.doi.org/10.1190/geo2017-0824.1.

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In statistical inverse problems, the objective is a complete statistical description of unknown parameters from noisy observations to quantify uncertainties in unknown parameters. We consider inverse problems with partial-differential-equation (PDE) constraints, which are applicable to many seismic problems. Bayesian inference is one of the most widely used approaches to precisely quantify statistics through a posterior distribution, incorporating uncertainties in observed data, modeling kernel, and prior knowledge of parameters. Typically when formulating the posterior distribution, the PDE constraints are required to be exactly satisfied, resulting in a highly nonlinear forward map and a posterior distribution with many local maxima. These drawbacks make it difficult to find an appropriate approximation for the posterior distribution. Another complicating factor is that traditional Markov chain Monte Carlo (MCMC) methods are known to converge slowly for realistically sized problems. To overcome these drawbacks, we relax the PDE constraints by introducing an auxiliary variable, which allows for Gaussian errors in the PDE and yields a bilinear posterior distribution with weak PDE constraints that is more amenable to uncertainty quantification because of its special structure. We determine that for a particular range of variance choices for the PDE misfit term, the new posterior distribution has fewer modes and can be well-approximated by a Gaussian distribution, which can then be sampled in a straightforward manner. Because it is prohibitively expensive to explicitly construct the dense covariance matrix of the Gaussian approximation for problems with more than [Formula: see text] unknowns, we have developed a method to implicitly construct it, which enables efficient sampling. We apply this framework to 2D seismic inverse problems with 1800 and 92,455 unknown parameters. The results illustrate that our framework can produce comparable statistical quantities with those produced by conventional MCMC-type methods while requiring far fewer PDE solves, which are the main computational bottlenecks in these problems.

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20

Liu, Junhong, Shanfang Huang, Xiaoyu Guo, Jiageng Wang, and Kan Wang. "INVERSE UNCERTAINTY QUANTIFICATION OF CTF PHYSICAL MODEL PARAMETERS USING BAYESIAN INFERENCE." Proceedings of the International Conference on Nuclear Engineering (ICONE) 2019.27 (2019): 1435. http://dx.doi.org/10.1299/jsmeicone.2019.27.1435.

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21

Faes, Matthias, Matteo Broggi, Edoardo Patelli, Yves Govers, John Mottershead, Michael Beer, and David Moens. "A multivariate interval approach for inverse uncertainty quantification with limited experimental data." Mechanical Systems and Signal Processing 118 (March 2019): 534–48. http://dx.doi.org/10.1016/j.ymssp.2018.08.050.

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de Vries, Kevin, Anna Nikishova, Benjamin Czaja, Gábor Závodszky, and Alfons G. Hoekstra. "INVERSE UNCERTAINTY QUANTIFICATION OF A CELL MODEL USING A GAUSSIAN PROCESS METAMODEL." International Journal for Uncertainty Quantification 10, no. 4 (2020): 333–49. http://dx.doi.org/10.1615/int.j.uncertaintyquantification.2020033186.

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23

Wu, Xu, Koroush Shirvan, and Tomasz Kozlowski. "Demonstration of the relationship between sensitivity and identifiability for inverse uncertainty quantification." Journal of Computational Physics 396 (November 2019): 12–30. http://dx.doi.org/10.1016/j.jcp.2019.06.032.

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Hu, Guojun, and Tomasz Kozlowski. "Inverse uncertainty quantification of trace physical model parameters using BFBT benchmark data." Annals of Nuclear Energy 96 (October 2016): 197–203. http://dx.doi.org/10.1016/j.anucene.2016.05.021.

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25

Berg, Steffen, Evren Unsal, and Harm Dijk. "Non-uniqueness and uncertainty quantification of relative permeability measurements by inverse modelling." Computers and Geotechnics 132 (April 2021): 103964. http://dx.doi.org/10.1016/j.compgeo.2020.103964.

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26

Bernardara, Pietro, Etienne de Rocquigny, Nicole Goutal, Aurélie Arnaud, and Giuseppe Passoni. "Uncertainty analysis in flood hazard assessment: hydrological and hydraulic calibrationThis article is one of a selection of papers published in this Special Issue on Hydrotechnical Engineering." Canadian Journal of Civil Engineering 37, no. 7 (July 2010): 968–79. http://dx.doi.org/10.1139/l10-056.

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Interest in the actual estimation of the uncertainty affecting flood hazard assessments is increasing within the scientific community and among decision makers. Several works may be found in the hydrological and hydraulic literature listing the sources of uncertainty affecting the estimation of extreme flood levels. Here, a well-assessed uncertainty treatment procedure is applied to carry out a complete flood hazard assessment study to encompass both the hydrological and hydraulic components. In particular, the focus is on modeling the sources of uncertainty via a direct (for discharge) or inverse (for roughness hydraulic coefficient) approach. The results illustrate the relative importance of the hydraulic and hydrological uncertainty sources on the final uncertainty. The solution of the inverse problem for the calibration of the roughness coefficient proves useful for several reasons, including the quantification of model error.

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Abdollahzadeh, Asaad, Alan Reynolds, Mike Christie, David Corne, Brian Davies, and Glyn Williams. "Bayesian Optimization Algorithm Applied to Uncertainty Quantification." SPE Journal 17, no. 03 (August 23, 2012): 865–73. http://dx.doi.org/10.2118/143290-pa.

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Summary Prudent decision making in subsurface assets requires reservoir uncertainty quantification. In a typical uncertainty-quantification study, reservoir models must be updated using the observed response from the reservoir by a process known as history matching. This involves solving an inverse problem, finding reservoir models that produce, under simulation, a similar response to that of the real reservoir. However, this requires multiple expensive multiphase-flow simulations. Thus, uncertainty-quantification studies employ optimization techniques to find acceptable models to be used in prediction. Different optimization algorithms and search strategies are presented in the literature, but they are generally unsatisfactory because of slow convergence to the optimal regions of the global search space, and, more importantly, failure in finding multiple acceptable reservoir models. In this context, a new approach is offered by estimation-of-distribution algorithms (EDAs). EDAs are population-based algorithms that use models to estimate the probability distribution of promising solutions and then generate new candidate solutions. This paper explores the application of EDAs, including univariate and multivariate models. We discuss two histogram-based univariate models and one multivariate model, the Bayesian optimization algorithm (BOA), which employs Bayesian networks for modeling. By considering possible interactions between variables and exploiting explicitly stored knowledge of such interactions, EDAs can accelerate the search process while preserving search diversity. Unlike most existing approaches applied to uncertainty quantification, the Bayesian network allows the BOA to build solutions using flexible rules learned from the models obtained, rather than fixed rules, leading to better solutions and improved convergence. The BOA is naturally suited to finding good solutions in complex high-dimensional spaces, such as those typical in reservoir-uncertainty quantification. We demonstrate the effectiveness of EDA by applying the well-known synthetic PUNQ-S3 case with multiple wells. This allows us to verify the methodology in a well-controlled case. Results show better estimation of uncertainty when compared with some other traditional population-based algorithms.

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Banks, H. T., Kathleen Holm, and Danielle Robbins. "Standard error computations for uncertainty quantification in inverse problems: Asymptotic theory vs. bootstrapping." Mathematical and Computer Modelling 52, no. 9-10 (November 2010): 1610–25. http://dx.doi.org/10.1016/j.mcm.2010.06.026.

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Polydorides, N. "A stochastic simulation method for uncertainty quantification in the linearized inverse conductivity problem." International Journal for Numerical Methods in Engineering 90, no. 1 (November 5, 2011): 22–39. http://dx.doi.org/10.1002/nme.3305.

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Zhang, Chi, Martin F. Lambert, Jinzhe Gong, Aaron C. Zecchin, Angus R. Simpson, and Mark L. Stephens. "Bayesian Inverse Transient Analysis for Pipeline Condition Assessment: Parameter Estimation and Uncertainty Quantification." Water Resources Management 34, no. 9 (June 10, 2020): 2807–20. http://dx.doi.org/10.1007/s11269-020-02582-9.

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Li, Weixuan, Guang Lin, and Bing Li. "Inverse regression-based uncertainty quantification algorithms for high-dimensional models: Theory and practice." Journal of Computational Physics 321 (September 2016): 259–78. http://dx.doi.org/10.1016/j.jcp.2016.05.040.

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Super, Ingrid, Stijn N. C. Dellaert, Antoon J. H. Visschedijk, and Hugo A. C. Denier van der Gon. "Uncertainty analysis of a European high-resolution emission inventory of CO<sub>2</sub> and CO to support inverse modelling and network design." Atmospheric Chemistry and Physics 20, no. 3 (February 14, 2020): 1795–816. http://dx.doi.org/10.5194/acp-20-1795-2020.

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Abstract. Quantification of greenhouse gas emissions is receiving a lot of attention because of its relevance for climate mitigation. Complementary to official reported bottom-up emission inventories, quantification can be done with an inverse modelling framework, combining atmospheric transport models, prior gridded emission inventories and a network of atmospheric observations to optimize the emission inventories. An important aspect of such a method is a correct quantification of the uncertainties in all aspects of the modelling framework. The uncertainties in gridded emission inventories are, however, not systematically analysed. In this work, a statistically coherent method is used to quantify the uncertainties in a high-resolution gridded emission inventory of CO2 and CO for Europe. We perform a range of Monte Carlo simulations to determine the effect of uncertainties in different inventory components, including the spatial and temporal distribution, on the uncertainty in total emissions and the resulting atmospheric mixing ratios. We find that the uncertainties in the total emissions for the selected domain are 1 % for CO2 and 6 % for CO. Introducing spatial disaggregation causes a significant increase in the uncertainty of up to 40 % for CO2 and 70 % for CO for specific grid cells. Using gridded uncertainties, specific regions can be defined that have the largest uncertainty in emissions and are thus an interesting target for inverse modellers. However, the largest sectors are usually the best-constrained ones (low relative uncertainty), so the absolute uncertainty is the best indicator for this. With this knowledge, areas can be identified that are most sensitive to the largest emission uncertainties, which supports network design.

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Ma, Xiaopeng, Kai Zhang, Liming Zhang, Chuanjin Yao, Jun Yao, Haochen Wang, Wang Jian, and Yongfei Yan. "Data-Driven Niching Differential Evolution with Adaptive Parameters Control for History Matching and Uncertainty Quantification." SPE Journal 26, no. 02 (January 21, 2021): 993–1010. http://dx.doi.org/10.2118/205014-pa.

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Summary History matching is a typical inverse problem that adjusts the uncertainty parameters of the reservoir numerical model with limited dynamic response data. In most situations, various parameter combinations can result in the same data fit, termed as nonuniqueness of inversion. It is desirable to find as many global or local optima as possible in a single optimization run, which may help to reveal the distribution of the uncertainty parameters in the posterior space, which is particularly important for robust optimization, risk analysis, and decision making in reservoir management. However, many factors, such as the nonlinearity of inversion problems and the time-consuming numerical simulation, limit the performance of most existing inverse algorithms. In this paper, we propose a novel data-driven niching differential evolution algorithm with adaptive parameter control for nonuniqueness of inversion, called DNDE-APC. On the basis of a differential evolution (DE) framework, the proposed algorithm integrates a clustering approach, niching technique, and local surrogate assistant method, which is designed to balance exploration and convergence in solving the multimodal inverse problems. Empirical studies on three benchmark problems demonstrate that the proposed algorithm is able to locate multiple solutions for complex multimodal problems on a limited computational budget. Integrated with convolutional variational autoencoder (CVAE) for parameterization of the high-dimensional uncertainty parameters, a history matching workflow is developed. The effectiveness of the proposed workflow is validated with heterogeneous waterflooding reservoir case studies. By analyzing the fitting and prediction of production data, history-matched realizations, the distribution of inversion parameters, and uncertainty quantization of forecasts, the results indicate that the new method can effectively tackle the nonuniqueness of inversion, and the prediction result is more robust.

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Dixon, J. R., B. A. Lindley, T. Taylor, and G. T. Parks. "DATA ASSIMILATION APPLIED TO PRESSURISED WATER REACTORS." EPJ Web of Conferences 247 (2021): 09020. http://dx.doi.org/10.1051/epjconf/202124709020.

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Best estimate plus uncertainty is the leading methodology to validate existing safety margins. It remains a challenge to develop and license these approaches, in part due to the high dimensionality of system codes. Uncertainty quantification is an active area of research to develop appropriate methods for propagating uncertainties, offering greater scientific reason, dimensionality reduction and minimising reliance on expert judgement. Inverse uncertainty quantification is required to infer a best estimate back on the input parameters and reduce the uncertainties, but it is challenging to capture the full covariance and sensitivity matrices. Bayesian inverse strategies remain attractive due to their predictive modelling and reduced uncertainty capabilities, leading to dramatic model improvements and validation of experiments. This paper uses state-of-the-art data assimilation techniques to obtain a best estimate of parameters critical to plant safety. Data assimilation can combine computational, benchmark and experimental measurements, propagate sparse covariance and sensitivity matrices, treat non-linear applications and accommodate discrepancies. The methodology is further demonstrated through application to hot zero power tests in a pressurised water reactor (PWR) performed using the BEAVRS benchmark with Latin hypercube sampling of reactor parameters to determine responses. WIMS 11 (dv23) and PANTHER (V.5:6:4) are used as the coupled neutronics and thermal-hydraulics codes; both are used extensively to model PWRs. Results demonstrate updated best estimate parameters and reduced uncertainties, with comparisons between posterior distributions generated using maximum entropy principle and cost functional minimisation techniques illustrated in recent conferences. Future work will improve the Bayesian inverse framework with the introduction of higher-order sensitivities.

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Stuart, A. M. "Inverse problems: A Bayesian perspective." Acta Numerica 19 (May 2010): 451–559. http://dx.doi.org/10.1017/s0962492910000061.

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The subject of inverse problems in differential equations is of enormous practical importance, and has also generated substantial mathematical and computational innovation. Typically some form of regularization is required to ameliorate ill-posed behaviour. In this article we review the Bayesian approach to regularization, developing a function space viewpoint on the subject. This approach allows for a full characterization of all possible solutions, and their relative probabilities, whilst simultaneously forcing significant modelling issues to be addressed in a clear and precise fashion. Although expensive to implement, this approach is starting to lie within the range of the available computational resources in many application areas. It also allows for the quantification of uncertainty and risk, something which is increasingly demanded by these applications. Furthermore, the approach is conceptually important for the understanding of simpler, computationally expedient approaches to inverse problems.

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Saibaba, Arvind K., and Peter K. Kitanidis. "Fast computation of uncertainty quantification measures in the geostatistical approach to solve inverse problems." Advances in Water Resources 82 (August 2015): 124–38. http://dx.doi.org/10.1016/j.advwatres.2015.04.012.

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Yun, Gun Jin, and Shen Shang. "A NEW INVERSE METHOD FOR THE UNCERTAINTY QUANTIFICATION OF SPATIALLY VARYING RANDOM MATERIAL PROPERTIES." International Journal for Uncertainty Quantification 6, no. 6 (2016): 515–31. http://dx.doi.org/10.1615/int.j.uncertaintyquantification.2016018673.

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Witteveen, Jeroen A. S., and Hester Bijl. "Transonic velocity fluctuations simulated using extremum diminishing uncertainty quantification based on inverse distance weighting." Theoretical and Computational Fluid Dynamics 26, no. 5 (July 6, 2011): 459–79. http://dx.doi.org/10.1007/s00162-011-0233-y.

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Colombo, Ivo, Giovanni M. Porta, Paolo Ruffo, and Alberto Guadagnini. "Uncertainty quantification of overpressure buildup through inverse modeling of compaction processes in sedimentary basins." Hydrogeology Journal 25, no. 2 (November 21, 2016): 385–403. http://dx.doi.org/10.1007/s10040-016-1493-9.

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Bledsoe, Keith C., Jason Hite, Matthew A. Jessee, and Jordan P. Lefebvre. "Application of Markov Chain Monte Carlo Methods for Uncertainty Quantification in Inverse Transport Problems." IEEE Transactions on Nuclear Science 68, no. 8 (August 2021): 2210–19. http://dx.doi.org/10.1109/tns.2021.3089018.

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DAO, TIEN TUAN, and MARIE-CHRISTINE HO BA THO. "A CONSISTENT DATA FUSION APPROACH FOR UNCERTAINTY QUANTIFICATION IN RIGID MUSCULOSKELETAL SIMULATION." Journal of Mechanics in Medicine and Biology 17, no. 04 (December 22, 2016): 1750062. http://dx.doi.org/10.1142/s0219519417500622.

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Uncertainty quantification in rigid musculoskeletal modeling is essential to analyze the risks related to the simulation outcomes. Data fusion from multiple sources is a potential solution to reduce data uncertainties. This present study aimed at proposing a new data fusion rule leading to a more consistent and coherent data for uncertainty quantification. Moreover, a new uncertainty representation was developed using imprecise probability approach. A biggest maximal coherent subsets (BMCS) operator was defined to fuse interval-valued data ranges from multiple sources. Fusion-based probability-box structure was developed to represent the data uncertainty. Case studies were performed for uncertainty propagation through inverse dynamics and static optimization algorithms. Hip joint moment and muscle force estimation were computed under effect of the uncertainties of thigh mass and muscle properties. Respective p-boxes of these properties were generated. Regarding the uncertainty propagation analysis, correlation coefficients showed a very good value ([Formula: see text]) for the proposed fusion operator according to classical operators. Muscle force variation of the rectus femoris was computed. Peak-to-peak (i.e., difference between maximal values) rectus femoris forces showed deviations of 55[Formula: see text]N and 40[Formula: see text]N for the first and second peaks, respectively. The development of the new fusion operator and fusion-based probability-box leads to a more consistent uncertainty quantification. This allows the estimation of risks associated with the simulation outcomes under input data uncertainties for rigid musculoskeletal modeling and simulation.

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Mondal, Anirban, and Jia Wei. "Bayesian Uncertainty Quantification for Channelized Reservoirs via Reduced Dimensional Parameterization." Mathematics 9, no. 9 (May 10, 2021): 1067. http://dx.doi.org/10.3390/math9091067.

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In this article, we study uncertainty quantification for flows in heterogeneous porous media. We use a Bayesian approach where the solution to the inverse problem is given by the posterior distribution of the permeability field given the flow and transport data. Permeability fields within facies are assumed to be described by two-point correlation functions, while interfaces that separate facies are represented via smooth pseudo-velocity fields in a level set formulation to get reduced dimensional parameterization. The permeability fields within facies and pseudo-velocity fields representing interfaces can be described using Karhunen–Loève (K-L) expansion, where one can select dominant modes. We study the error of posterior distributions introduced in such truncations by estimating the difference in the expectation of a function with respect to full and truncated posteriors. The theoretical result shows that this error can be bounded by the tail of K-L eigenvalues with constants independent of the dimension of discretization. This result guarantees the feasibility of such truncations with respect to posterior distributions. To speed up Bayesian computations, we use an efficient two-stage Markov chain Monte Carlo (MCMC) method that utilizes mixed multiscale finite element method (MsFEM) to screen the proposals. The numerical results show the validity of the proposed parameterization to channel geometry and error estimations.

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Cho, Taewon, Hodjat Pendar, and Julianne Chung. "Computational tools for inversion and uncertainty estimation in respirometry." PLOS ONE 16, no. 5 (May 21, 2021): e0251926. http://dx.doi.org/10.1371/journal.pone.0251926.

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In many physiological systems, real-time endogeneous and exogenous signals in living organisms provide critical information and interpretations of physiological functions; however, these signals or variables of interest are not directly accessible and must be estimated from noisy, measured signals. In this paper, we study an inverse problem of recovering gas exchange signals of animals placed in a flow-through respirometry chamber from measured gas concentrations. For large-scale experiments (e.g., long scans with high sampling rate) that have many uncertainties (e.g., noise in the observations or an unknown impulse response function), this is a computationally challenging inverse problem. We first describe various computational tools that can be used for respirometry reconstruction and uncertainty quantification when the impulse response function is known. Then, we address the more challenging problem where the impulse response function is not known or only partially known. We describe nonlinear optimization methods for reconstruction, where both the unknown model parameters and the unknown signal are reconstructed simultaneously. Numerical experiments show the benefits and potential impacts of these methods in respirometry.

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Price, M. A., J. D. McEwen, X. Cai, and T. D. Kitching (for the LSST Dark Energy Science Collaboration). "Sparse Bayesian mass mapping with uncertainties: peak statistics and feature locations." Monthly Notices of the Royal Astronomical Society 489, no. 3 (August 26, 2019): 3236–50. http://dx.doi.org/10.1093/mnras/stz2373.

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ABSTRACT Weak lensing convergence maps – upon which higher order statistics can be calculated – can be recovered from observations of the shear field by solving the lensing inverse problem. For typical surveys this inverse problem is ill-posed (often seriously) leading to substantial uncertainty on the recovered convergence maps. In this paper we propose novel methods for quantifying the Bayesian uncertainty in the location of recovered features and the uncertainty in the cumulative peak statistic – the peak count as a function of signal-to-noise ratio (SNR). We adopt the sparse hierarchical Bayesian mass-mapping framework developed in previous work, which provides robust reconstructions and principled statistical interpretation of reconstructed convergence maps without the need to assume or impose Gaussianity. We demonstrate our uncertainty quantification techniques on both Bolshoi N-body (cluster scale) and Buzzard V-1.6 (large-scale structure) N-body simulations. For the first time, this methodology allows one to recover approximate Bayesian upper and lower limits on the cumulative peak statistic at well-defined confidence levels.

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Wu, Xu, Travis Mui, Guojun Hu, Hadi Meidani, and Tomasz Kozlowski. "Inverse uncertainty quantification of TRACE physical model parameters using sparse gird stochastic collocation surrogate model." Nuclear Engineering and Design 319 (August 2017): 185–200. http://dx.doi.org/10.1016/j.nucengdes.2017.05.011.

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Wu, Xu, Tomasz Kozlowski, Hadi Meidani, and Koroush Shirvan. "Inverse uncertainty quantification using the modular Bayesian approach based on Gaussian process, Part 1: Theory." Nuclear Engineering and Design 335 (August 2018): 339–55. http://dx.doi.org/10.1016/j.nucengdes.2018.06.004.

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Jasra, Ajay, Kody J. H. Law, and Yan Zhou. "FORWARD AND INVERSE UNCERTAINTY QUANTIFICATION USING MULTILEVEL MONTE CARLO ALGORITHMS FOR AN ELLIPTIC NONLOCAL EQUATION." International Journal for Uncertainty Quantification 6, no. 6 (2016): 501–14. http://dx.doi.org/10.1615/int.j.uncertaintyquantification.2016018661.

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Butler, T., J. Jakeman, and T. Wildey. "Convergence of Probability Densities Using Approximate Models for Forward and Inverse Problems in Uncertainty Quantification." SIAM Journal on Scientific Computing 40, no. 5 (January 2018): A3523—A3548. http://dx.doi.org/10.1137/18m1181675.

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Abu Saleem, Rabie A., and Tomasz Kozlowski. "Effect of mesh refinement on the estimation of model input parameters using Inverse Uncertainty Quantification." Annals of Nuclear Energy 132 (October 2019): 271–76. http://dx.doi.org/10.1016/j.anucene.2019.04.044.

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Dostert, P., Y. Efendiev, and B. Mohanty. "Efficient uncertainty quantification techniques in inverse problems for Richards’ equation using coarse-scale simulation models." Advances in Water Resources 32, no. 3 (March 2009): 329–39. http://dx.doi.org/10.1016/j.advwatres.2008.11.009.

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