Download or read book Novel Algorithms for Uncertainty Quantification in Large Scale Systems written by Siddhant Wahal and published by . This book was released on 2020 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty Quantification (UQ) algorithms are of increasing significance in science and engineering. The process of modeling physical reality on computers is rife with uncertainties. These uncertainties get propagated through the computer model, leading to uncertain outputs. As decision-makers from every facet of society come to increasingly rely on computer predictions, the need to characterize this uncertainty has never been greater. However, doing so efficiently remains challenging. This is primarily because computer models are often time consuming to run and because their inputs live in high-dimensional spaces that are difficult to explore. In this thesis, we seek to address this challenge in the context of two UQ problems. In the first UQ problem, we study rare-event simulation: given a smooth non-linear map with uncertain inputs, what is the probability that the output evaluates inside a specified interval? Standard statistical approaches for computing this probability, such as the Monte Carlo method, become computationally inefficient as the event under consideration becomes rare. To address this inefficiency, we present two Importance Sampling (IS) algorithms. Our first algorithm, called the Bayesian Inverse Monte Carlo (BIMC) method, relies on solving a fictitious Bayesian inverse problem. The solution of the inverse problem yields a posterior PDF, a local Gaussian approximation to which serves as the importance sampling density. We subject BIMC to rigorous theoretical and experimental analysis, which establishes that BIMC can lead to speedups of several orders-of-magnitude (over the Monte Carlo method) when the forward map is nearly affine, or weakly non-linear. When these conditions are violated, that is, when the forward map is significantly nonlinear, BIMC leads to a poor-quality IS distribution. Motivated by these limitations, we propose modifications to BIMC. The modified algorithm, which we term Adaptive-BIMC (A-BIMC), proceeds in two stages. The first stage roughly identifies those regions in input space that trigger a rare event. The second stage then refines the approximation from the first stage of the algorithm. We study A-BIMC’s performance on synthetic problems and demonstrate that its performance doesn’t depend on how small the target probability is. Rather it depends on the nonlinearity of the input-output map. Through these experiments, we also find that A-BIMC’s performance deteriorates with increasing ambient dimensionality of the problem. To address this issue, we lay the foundation for a general dimension reduction strategy for rare-event probability estimation. The second UQ problem concerns the statistical calibration of model inputs from observed data, with the ultimate aim of issuing uncertainty-equipped predictions of a Quantity-of- Interest (QoI). The physical system that we study here is a hydrocarbon reservoir containing geological faults. Operational decisions concerning the reservoir rely on predictions of financial summaries of the reservoir, such as its Net Present Value. These summaries depend on the nature of fluid flow within the reservoir, which is itself controlled by the extent to which an individual fault inhibits or facilitates flow. This fault property, known as the fault transmissibility, isn’t directly measurable and must be calibrated using production data. Here, we design and analyze a complete data-to-prediction workflow to quantify post-calibration uncertainties. We also discuss how these uncertainties change under different reservoir conditions

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 Efficient Algorithms for Uncertainty Quantification Using Polynomial Chaos Expansion and Its Applications to Composite Structures written by Mishal Thapa and published by . This book was released on 2019 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty Quantification (UQ) deals with the study of variation in the response due to the presence of uncertainties in input parameters and governing models. Among the prevalent probabilistic techniques for UQ, non-intrusive Polynomial Chaos Expansion (PCE) has become more popular recently due to its mean square convergence property and ability to integrate deterministic codes as black-box. However, the number of basis terms in the expansion increases exponentially with the number of random inputs - 'curse of dimensionality,' and demands a huge number of function evaluations. Hence, this dissertation has attempted to extensively explore new robust algorithms for PCE while maintaining a proper balance between accuracy and computational efficiency. At first, a new non-intrusive method for PCE called Polynomial Chaos Decomposition with Differentiation (PCDD) is developed. The PCDD utilizes higher-order sensitivities of the responses and requires samples equal to the number of basis terms only. Secondly, the PCDD is utilized to develop a stochastic multi-scale modeling framework for composite structures since the response of composites is hugely influenced by the uncertainties existing at different scales such as micro-scale and macro-scale. Another framework for stochastic progressive failure analysis (PFA) of composites is also developed that allows performing global sensitivity analysis (GSA) to identify the relative importance of random inputs as a post-processing step. To further reduce the number of samples and make the stochastic problem more tractable, an adaptive L2-minimization algorithm that allows basis adaptivity along with sequential adaptive sampling is developed. Finally, an adaptive algorithm to obtain sparse PCE models with L1-minimization and sequential sampling is also proposed for high-dimensional problems. The L1-minimization is capable of solving the under-determined system when the number of samples is minuscule. It is also advantageous in terms of computational storage and memory because of its ability to provide a sparse solution. In general, the overarching goal of obtaining high-fidelity stochastic response models while maintaining a balance between accuracy and computational cost was successfully achieved by the novel algorithms developed in this dissertation. Furthermore, the invaluable information obtained with PCE for composite structures highlighted the benefits of its implementation in engineering problems.

Download or read book Data Driven Uncertainty Quantification for Large Scale Simulations written by Fabian Franzelin and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Novel Probabilistic and Distributed Algorithms for Guidance Control and Nonlinear Estimation of Large scale Multi agent Systems written by Saptarshi Bandyopadhyay and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Handbook of Research on Novel Soft Computing Intelligent Algorithms written by Pandian Vasant and published by IGI Global. This book was released on 2013-08-31 with total page 1173 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book explores emerging technologies and best practices designed to effectively address concerns inherent in properly optimizing advanced systems, demonstrating applications in areas such as bio-engineering, space exploration, industrial informatics, information security, and nuclear and renewable energies"--Provided by publisher.

Download or read book Uncertainty Quantification written by Ralph C. Smith and published by SIAM. This book was released on 2024-09-13 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncertainty quantification serves a fundamental role when establishing the predictive capabilities of simulation models. This book provides a comprehensive and unified treatment of the mathematical, statistical, and computational theory and methods employed to quantify uncertainties associated with models from a wide range of applications. Expanded and reorganized, the second edition includes advances in the field and provides a comprehensive sensitivity analysis and uncertainty quantification framework for models from science and engineering. It contains new chapters on random field representations, observation models, parameter identifiability and influence, active subspace analysis, and statistical surrogate models, and a completely revised chapter on local sensitivity analysis. Other updates to the second edition are the inclusion of over 100 exercises and many new examples — several of which include data — and UQ Crimes listed throughout the text to identify common misconceptions and guide readers entering the field. Uncertainty Quantification: Theory, Implementation, and Applications, Second Edition is intended for advanced undergraduate and graduate students as well as researchers in mathematics, statistics, engineering, physical and biological sciences, operations research, and computer science. Readers are assumed to have a basic knowledge of probability, linear algebra, differential equations, and introductory numerical analysis. The book can be used as a primary text for a one-semester course on sensitivity analysis and uncertainty quantification or as a supplementary text for courses on surrogate and reduced-order model construction and parameter identifiability analysis.

Download or read book Efficient Non intrusive Uncertainty Quantification for Large scale Simulation Scenarios written by Florian Künzner and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Uncertainty Quantification written by Christian Soize and published by Springer. This book was released on 2018-07-25 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the fundamental notions and advanced mathematical tools in the stochastic modeling of uncertainties and their quantification for large-scale computational models in sciences and engineering. In particular, it focuses in parametric uncertainties, and non-parametric uncertainties with applications from the structural dynamics and vibroacoustics of complex mechanical systems, from micromechanics and multiscale mechanics of heterogeneous materials. Resulting from a course developed by the author, the book begins with a description of the fundamental mathematical tools of probability and statistics that are directly useful for uncertainty quantification. It proceeds with a well carried out description of some basic and advanced methods for constructing stochastic models of uncertainties, paying particular attention to the problem of calibrating and identifying a stochastic model of uncertainty when experimental data is available. This book is intended to be a graduate-level textbook for students as well as professionals interested in the theory, computation, and applications of risk and prediction in science and engineering fields.

Download or read book Handbook of Uncertainty Quantification written by Roger Ghanem and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Introduction to uncertainty quantification written by T. J. Sullivan and published by . This book was released on 2015 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book New Algorithms for Uncertainty Quantification and Nonlinear Estimation of Stochastic Dynamical Systems written by Parikshit Dutta and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Recently there has been growing interest to characterize and reduce uncertainty in stochastic dynamical systems. This drive arises out of need to manage uncertainty in complex, high dimensional physical systems. Traditional techniques of uncertainty quantification (UQ) use local linearization of dynamics and assumes Gaussian probability evolution. But several difficulties arise when these UQ models are applied to real world problems, which, generally are nonlinear in nature. Hence, to improve performance, robust algorithms, which can work efficiently in a nonlinear non-Gaussian setting are desired. The main focus of this dissertation is to develop UQ algorithms for nonlinear systems, where uncertainty evolves in a non-Gaussian manner. The algorithms developed are then applied to state estimation of real-world systems. The first part of the dissertation focuses on using polynomial chaos (PC) for uncertainty propagation, and then achieving the estimation task by the use of higher order moment updates and Bayes rule. The second part mainly deals with Frobenius-Perron (FP) operator theory, how it can be used to propagate uncertainty in dynamical systems, and then using it to estimate states by the use of Bayesian update. Finally, a method to represent the process noise in a stochastic dynamical system using a nite term Karhunen-Loeve (KL) expansion is proposed. The uncertainty in the resulting approximated system is propagated using FP operator. The performance of the PC based estimation algorithms were compared with extended Kalman filter (EKF) and unscented Kalman filter (UKF), and the FP operator based techniques were compared with particle filters, when applied to a duffing oscillator system and hypersonic reentry of a vehicle in the atmosphere of Mars. It was found that the accuracy of the PC based estimators is higher than EKF or UKF and the FP operator based estimators were computationally superior to the particle filtering algorithms.

Download or read book A Decomposition based Approach to Uncertainty Quantification of Multicomponent Systems written by Sergio Daniel Marques Amaral and published by . This book was released on 2015 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: To support effective decision making, engineers should comprehend and manage various uncertainties throughout the design process. In today's modern systems, quantifying uncertainty can become cumbersome and computationally intractable for one individual or group to manage. This is particularly true for systems comprised of a large number of components. In many cases, these components may be developed by different groups and even run on different computational platforms, making it challenging or even impossible to achieve tight integration of the various models. This thesis presents an approach for overcoming this challenge by establishing a divide-and-conquer methodology, inspired by the decomposition-based approaches used in multidisciplinary analysis and optimization. Specifically, this research focuses on uncertainty analysis, also known as forward propagation of uncertainties, and sensitivity analysis. We present an approach for decomposing the uncertainty analysis task amongst the various components comprising a feed-forward system and synthesizing the local uncertainty analyses into a system uncertainty analysis. Our proposed decomposition-based multicomponent uncertainty analysis approach is shown to converge in distribution to the traditional all-at-once Monte Carlo uncertainty analysis under certain conditions. Our decomposition-based sensitivity analysis approach, which is founded on our decomposition-based uncertainty analysis algorithm, apportions the system output variance among the system inputs. The proposed decomposition-based uncertainty quantification approach is demonstrated on a multidisciplinary gas turbine system and is compared to the traditional all-at-once Monte Carlo uncertainty quantification approach. To extend the decomposition-based uncertainty quantification approach to high dimensions, this thesis proposes a novel optimization formulation to estimate statistics from a target distribution using random samples generated from a (different) proposal distribution. The proposed approach employs the well-defined and determinable empirical distribution function associated with the available samples. The resulting optimization problem is shown to be a single linear equality and box-constrained quadratic program and can be solved efficiently using optimization algorithms that scale well to high dimensions. Under some conditions restricting the class of distribution functions, the solution of the optimization problem yields importance weights that are shown to result in convergence in the Ll-norm of the weighted proposal empirical distribution function to the target distribution function, as the number of samples tends to infinity. Results on a variety of test cases show that the proposed approach performs well in comparison with other well-known approaches. The proposed approaches presented herein are demonstrated on a realistic application; environmental impacts of aviation technologies and operations. The results demonstrate that the decomposition-based uncertainty quantification approach can effectively quantify the uncertainty of a multicomponent system for which the models are housed in different locations and owned by different groups.

Download or read book Handbook of Probabilistic Models written by Pijush Samui and published by Butterworth-Heinemann. This book was released on 2019-10-05 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Probabilistic Models carefully examines the application of advanced probabilistic models in conventional engineering fields. In this comprehensive handbook, practitioners, researchers and scientists will find detailed explanations of technical concepts, applications of the proposed methods, and the respective scientific approaches needed to solve the problem. This book provides an interdisciplinary approach that creates advanced probabilistic models for engineering fields, ranging from conventional fields of mechanical engineering and civil engineering, to electronics, electrical, earth sciences, climate, agriculture, water resource, mathematical sciences and computer sciences. Specific topics covered include minimax probability machine regression, stochastic finite element method, relevance vector machine, logistic regression, Monte Carlo simulations, random matrix, Gaussian process regression, Kalman filter, stochastic optimization, maximum likelihood, Bayesian inference, Bayesian update, kriging, copula-statistical models, and more. Explains the application of advanced probabilistic models encompassing multidisciplinary research Applies probabilistic modeling to emerging areas in engineering Provides an interdisciplinary approach to probabilistic models and their applications, thus solving a wide range of practical problems

Download or read book 2014 5th Workshop on Latest Advances in Scalable Algorithms for Large Scale Systems ScalA 2014 written by Vassil Alexandrov and published by . This book was released on 2014 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Bayesian Reinforcement Learning written by Mohammad Ghavamzadeh and published by . This book was released on 2015-11-18 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bayesian methods for machine learning have been widely investigated, yielding principled methods for incorporating prior information into inference algorithms. This monograph provides the reader with an in-depth review of the role of Bayesian methods for the reinforcement learning (RL) paradigm. The major incentives for incorporating Bayesian reasoning in RL are that it provides an elegant approach to action-selection (exploration/exploitation) as a function of the uncertainty in learning, and it provides a machinery to incorporate prior knowledge into the algorithms. Bayesian Reinforcement Learning: A Survey first discusses models and methods for Bayesian inference in the simple single-step Bandit model. It then reviews the extensive recent literature on Bayesian methods for model-based RL, where prior information can be expressed on the parameters of the Markov model. It also presents Bayesian methods for model-free RL, where priors are expressed over the value function or policy class. Bayesian Reinforcement Learning: A Survey is a comprehensive reference for students and researchers with an interest in Bayesian RL algorithms and their theoretical and empirical properties.

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.