Download or read book Uncertainty Quantification and Propagation in Materials Modeling Using a Bayesian Inferential Framework written by Denielle E. Ricciardi and published by . This book was released on 2020 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: Achieving a statistical confidence in a simulation output requires, first, the identification of the various sources of error and uncertainty affecting the simulation results. These sources include machine and user error in collecting calibration data, uncertain model parameters, random error from natural processes, and model inadequacy in capturing the true material property or behavior. Statistical inference can then be used to recover information about unknown model parameters by conditioning on available data while taking into account the various sources of uncertainty.

Download or read book Uncertainty Quantification in Multiscale Materials Modeling written by Yan Wang and published by Woodhead Publishing Limited. This book was released on 2020-03-12 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty Quantification in Multiscale Materials Modeling provides a complete overview of uncertainty quantification (UQ) in computational materials science. It provides practical tools and methods along with examples of their application to problems in materials modeling. UQ methods are applied to various multiscale models ranging from the nanoscale to macroscale. This book presents a thorough synthesis of the state-of-the-art in UQ methods for materials modeling, including Bayesian inference, surrogate modeling, random fields, interval analysis, and sensitivity analysis, providing insight into the unique characteristics of models framed at each scale, as well as common issues in modeling across scales.

Download or read book Uncertainty Quantification written by Ralph C. Smith and published by SIAM. This book was released on 2013-12-02 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of uncertainty quantification is evolving rapidly because of increasing emphasis on models that require quantified uncertainties for large-scale applications, novel algorithm development, and new computational architectures that facilitate implementation of these algorithms. Uncertainty Quantification: Theory, Implementation, and Applications provides readers with the basic concepts, theory, and algorithms necessary to quantify input and response uncertainties for simulation models arising in a broad range of disciplines. The book begins with a detailed discussion of applications where uncertainty quantification is critical for both scientific understanding and policy. It then covers concepts from probability and statistics, parameter selection techniques, frequentist and Bayesian model calibration, propagation of uncertainties, quantification of model discrepancy, surrogate model construction, and local and global sensitivity analysis. The author maintains a complementary web page where readers can find data used in the exercises and other supplementary material.

Download or read book Prediction Using Numerical Simulations A Bayesian Framework for Uncertainty Quantification and Its Statistical Challenge written by and published by . This book was released on 2002 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertain quantification is essential in using numerical models for prediction. While many works focused on how the uncertainty of the inputs propagate to the outputs, the modeling errors of the numerical model were often overlooked. In our Bayesian framework, modeling errors play an essential role and were assessed through studying numerical solution errors. The main ideas and key concepts will be illustrated through an oil reservoir case study. In this study, inference on the input has to be made from the output. Bayesian analysis is adopted to handle this inverse problem, then combine it with the forward simulation for prediction. The solution error models were established based on the scale-up solutions and fine-grid solutions. As the central piece of our framework, the robustness of these error models is fundamental. In addition to the oil reservoir computer codes, we will also discuss the modelling of solution error of shock wave physics.

Download or read book Uncertainty Quantification with R written by Eduardo Souza de Cursi and published by Springer Nature. This book was released on with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Model Validation and Uncertainty Quantification Volume 3 written by Zhu Mao and published by Springer Nature. This book was released on 2022-07-01 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model Validation and Uncertainty Quantification, Volume 3: Proceedings of the 40th IMAC, A Conference and Exposition on Structural Dynamics, 2022, the third volume of nine from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Model Validation and Uncertainty Quantification, including papers on: Uncertainty Quantification and Propagation in Structural Dynamics Bayesian Analysis for Real-Time Monitoring and Maintenance Uncertainty in Early Stage Design Quantification of Model-Form Uncertainties Fusion of Test and Analysis MVUQ in Action

Download or read book Bayesian Uncertainty Quantification for Functional Response written by Xiao Guo and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This chapter addresses the stochastic modeling of functional response, which is a major concern in engineering implementation. We first introduce a general framework and several conventional models for functional data, including the functional linear model, penalized regression splines, and the spatial temporal model. However, in engineering practice, a naive mathematical modeling of functional response may fail due to the lack of expressing the underlying physical mechanism. We propose a series of quasiphysical models to handle the functional response. A motivating example of metamaterial design is thoroughly discussed to demonstrate the idea of quasiphysical models. In real applications, various uncertainties have to be taken into account, such as that of the permittivity or permeability of the substrate of the metamaterial. For the propagation of uncertainty, simulation-based methods are discussed. A Bayesian framework is presented to deal with the model calibration in the case of functional response. Experimental results illustrate the efficiency of the proposed method.

Download or read book Handbook of Uncertainty Quantification written by Roger Ghanem and published by Springer. This book was released on 2016-05-08 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topic of Uncertainty Quantification (UQ) has witnessed massive developments in response to the promise of achieving risk mitigation through scientific prediction. It has led to the integration of ideas from mathematics, statistics and engineering being used to lend credence to predictive assessments of risk but also to design actions (by engineers, scientists and investors) that are consistent with risk aversion. The objective of this Handbook is to facilitate the dissemination of the forefront of UQ ideas to their audiences. We recognize that these audiences are varied, with interests ranging from theory to application, and from research to development and even execution.

Download or read book Framework for Analysis and Identification of Nonlinear Distributed Parameter Systems using Bayesian Uncertainty Quantification based on Generalized Polynomial Chaos written by Janya-anurak, Chettapong and published by KIT Scientific Publishing. This book was released on 2017-04-04 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work, the Uncertainty Quantification (UQ) approaches combined systematically to analyze and identify systems. The generalized Polynomial Chaos (gPC) expansion is applied to reduce the computational effort. The framework using gPC based on Bayesian UQ proposed in this work is capable of analyzing the system systematically and reducing the disagreement between the model predictions and the measurements of the real processes to fulfill user defined performance criteria.

Download or read book Uncertainty Quantification and Model Calibration written by Jan Peter Hessling and published by BoD – Books on Demand. This book was released on 2017-07-05 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty quantification may appear daunting for practitioners due to its inherent complexity but can be intriguing and rewarding for anyone with mathematical ambitions and genuine concern for modeling quality. Uncertainty quantification is what remains to be done when too much credibility has been invested in deterministic analyses and unwarranted assumptions. Model calibration describes the inverse operation targeting optimal prediction and refers to inference of best uncertain model estimates from experimental calibration data. The limited applicability of most state-of-the-art approaches to many of the large and complex calculations made today makes uncertainty quantification and model calibration major topics open for debate, with rapidly growing interest from both science and technology, addressing subtle questions such as credible predictions of climate heating.

Download or read book Bayesian Inference and Uncertainty Propagation in Dynamical Systems written by Umamaheswara Konda Venkata and published by . This book was released on 2010 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: Decision making is based on our models of what we expect to observe. Apart from the underlying models, the real-time observations or measurements are another important source for predictive inference. Typically, these models and observations are noisy, whose uncertainty can be characterized using probability distributions. The Bayesian framework provides a principled basis to combine such uncertain models and noisy measurements. The dissertation focuses mainly on data assimilation methods in puff-based Lagrangian dispersion models and uncertainty propagation in dynamic models. Real-time tracking and prediction of chemical and biological releases are important for fast response to chemical and biological accidents and attacks.^In a chemical release incident, the important questions that arise in hazard prediction and assessment are: Where are the sources? Where are the toxic plumes going? The two sources for predictive inference with which to address these questions are the relevant dispersion models and concentration data. In this dissertation, data assimilation is studied in the context of puff-based Lagrangian chem-bio atmospheric dispersion models. For the estimation of plume evolution, an Extended Kalman filter and a particle filter are designed for a representative puff-based dispersion model and the results are discussed. The application of particle filters in a variable dimension state space model and its potential for various puff-based atmospheric dispersion modeling packages is demonstrated. A novel grid-based algorithm is presented for efficient source identification, where the number of sources, locations and strengths are unknown.^The source identification problem is formulated as a convex optimization problem in the L1 metric, which exploits the sparse nature of the solution to efficiently estimate the source characteristics, even when the number of sources is large. Dispersion is a complex nonlinear physical process with numerous uncertainties in model parameters, source parameters, and initial conditions. Accurate propagation of these uncertainties through the models is crucial for a reliable prediction of the probability distribution of the states and assessment of risk. The problem of uncertainty propagation and sensitivity analysis in nonlinear puff-based dispersion models is addressed using stochastic spectral methods based on polynomial chaos (PC) series expansions of random processes.^A wide class of probability distributions can be represented using this approach. While the existing methods work very well and even provide exact description of the uncertainty propagation for linear dynamical systems subject to either initial condition and temporal stochastic disturbance modeled as white noise process or time-invariant parametric uncertainty, the main challenge lies in characterizing the uncertainty in the system states due to both parametric and temporal stochastic uncertainties simultaneously. A hybrid Bayesian-PC based approach is proposed to address this general problem of uncertainty propagation in linear dynamical systems with random inputs and uncertain model parameters. This approach is further extended to address the filtering problem, when there is parametric uncertainty.

Download or read book Novel Uncertainty Quantification Techniques for Problems Described by Stochastic Partial Differential Equations written by Peng Chen and published by . This book was released on 2014 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty propagation (UP) in physical systems governed by PDEs is a challenging problem. This thesis addresses the development of a number of innovative techniques that emphasize the need for high-dimensionality modeling, resolving discontinuities in the stochastic space and considering the computational expense of forward solvers. Both Bayesian and non-Bayesian approaches are considered. Applications demonstrating the developed techniques are investigated in the context of flow in porous media and reservoir engineering applications. An adaptive locally weighted projection method (ALWPR) is firstly developed. It adaptively selects the needed runs of the forward solver (data collection) to maximize the predictive capability of the method. The methodology effectively learns the local features and accurately quantifies the uncertainty in the prediction of the statistics. It could provide predictions and confidence intervals at any query input and can deal with multi-output responses. A probabilistic graphical model framework for uncertainty quantification is next introduced. The high dimensionality issue of the input is addressed by a local model reduction framework. Then the conditional distribution of the multi-output responses on the low dimensional representation of the input field is factorized into a product of local potential functions that are represented non-parametrically. A nonparametric loopy belief propagation algorithm is developed for studying uncertainty quantification directly on the graph. The nonparametric nature of the model is able to efficiently capture non-Gaussian features of the response. Finally an infinite mixture of Multi-output Gaussian Process (MGP) models is presented to effectively deal with many of the difficulties of current UQ methods. This model involves an infinite mixture of MGP's using Dirichlet process priors and is trained using Variational Bayesian Inference. The Bayesian nature of the model allows for the quantification of the uncertainties due to the limited number of simulations. The automatic detection of the mixture components by the Variational Inference algorithm is able to capture discontinuities and localized features without adhering to ad hoc constructions. Finally, correlations between the components of multi-variate responses are captured by the underlying MGP model in a natural way. A summary of suggestions for future research in the area of uncertainty quantification field are given at the end of the thesis.

Download or read book Uncertainty Quantification in Multiscale Materials Modeling written by Yan Wang and published by Woodhead Publishing. This book was released on 2020-03-10 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty Quantification in Multiscale Materials Modeling provides a complete overview of uncertainty quantification (UQ) in computational materials science. It provides practical tools and methods along with examples of their application to problems in materials modeling. UQ methods are applied to various multiscale models ranging from the nanoscale to macroscale. This book presents a thorough synthesis of the state-of-the-art in UQ methods for materials modeling, including Bayesian inference, surrogate modeling, random fields, interval analysis, and sensitivity analysis, providing insight into the unique characteristics of models framed at each scale, as well as common issues in modeling across scales. Synthesizes available UQ methods for materials modeling Provides practical tools and examples for problem solving in modeling material behavior across various length scales Demonstrates UQ in density functional theory, molecular dynamics, kinetic Monte Carlo, phase field, finite element method, multiscale modeling, and to support decision making in materials design Covers quantum, atomistic, mesoscale, and engineering structure-level modeling and simulation

Download or read book Model Validation and Uncertainty Quantification Volume 3 written by Robert Barthorpe and published by Springer. This book was released on 2018-07-30 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: Model Validation and Uncertainty Quantification, Volume 3: Proceedings of the 36th IMAC, A Conference and Exposition on Structural Dynamics, 2018, the third volume of nine from the Conference brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Model Validation and Uncertainty Quantification, including papers on: Uncertainty Quantification in Material Models Uncertainty Propagation in Structural Dynamics Practical Applications of MVUQ Advances in Model Validation & Uncertainty Quantification: Model Updating Model Validation & Uncertainty Quantification: Industrial Applications Controlling Uncertainty Uncertainty in Early Stage Design Modeling of Musical Instruments Overview of Model Validation and Uncertainty

Download or read book Uncertainty in Engineering written by Louis J. M. Aslett and published by Springer Nature. This book was released on 2022 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book provides an introduction to uncertainty quantification in engineering. Starting with preliminaries on Bayesian statistics and Monte Carlo methods, followed by material on imprecise probabilities, it then focuses on reliability theory and simulation methods for complex systems. The final two chapters discuss various aspects of aerospace engineering, considering stochastic model updating from an imprecise Bayesian perspective, and uncertainty quantification for aerospace flight modelling. Written by experts in the subject, and based on lectures given at the Second Training School of the European Research and Training Network UTOPIAE (Uncertainty Treatment and Optimization in Aerospace Engineering), which took place at Durham University (United Kingdom) from 2 to 6 July 2018, the book offers an essential resource for students as well as scientists and practitioners.

Download or read book Bayesian and Frequentist Methods for Uncertainty Quantification and Interpretation in Statistical and Machine Learning Models written by Junting Ren and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern statistical and machine learning models excel at capturing complex non-linear relationships between outcomes and predictors, resulting in high accuracy. However, the complexity of these models can impede statistical inference and interpretation. This dissertation confronts and tries to overcome the emerging challenges presented by intricate models and big data. One significant challenge involves modeling and statistical inference for zero-inflated semi-continuous data. Thus, in the first part, we develop a flexible Bayesian semi-parametric mixture model for zero-inflated skewed longitudinal data, generating credible intervals for not only the mean but also any quantiles of the parameters and predictions, aiding population inference of skewed data. The model is applied to evaluate how number of binge drinking episodes changes with neuromaturation using the National Consortium on Alcohol and Neuro-Development in Adolescence data. On the other hand, credible or confidence intervals do not directly address a common question: can we identify a subset of predictions or parameters with true values exceeding a specific threshold with confidence? To tackle this, in the second part, we improve upon the inverse set estimation framework that estimates such sets by developing an approach with fewer assumptions and broader applicability to various data settings. We construct an excursion set map with probability guarantee on the North American Regional Climate Change Assessment Program data using the proposed method. Moreover, we use this new method to discover characteristics of in-patients at high risk for severe outcomes using University of California San Diego hospital data. In the third part, we apply this inverse set estimation inference framework to quantify prediction model uncertainty and develop theories and algorithms that ensure non-conservative coverage rates for a single threshold in non-asymptotic settings in regression problems. We demonstrate the effectiveness of the constructed confidence sets for uncertainty quantification and interpretation in both simulate data and PhysioNet sepsis prediction data.

Download or read book Methodology for Characterizing Modeling and Discretization Uncertainties in Computational Simulation written by and published by . This book was released on 2000 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research effort focuses on methodology for quantifying the effects of model uncertainty and discretization error on computational modeling and simulation. The work is directed towards developing methodologies which treat model form assumptions within an overall framework for uncertainty quantification, for the purpose of developing estimates of total prediction uncertainty. The present effort consists of work in three areas: framework development for sources of uncertainty and error in the modeling and simulation process which impact model structure; model uncertainty assessment and propagation through Bayesian inference methods; and discretization error estimation within the context of non-deterministic analysis.