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Author: Dan Gabriel Cacuci Publisher: Springer ISBN: 366258395X Category : Technology & Engineering Languages : en Pages : 451
Book Description
This book addresses the experimental calibration of best-estimate numerical simulation models. The results of measurements and computations are never exact. Therefore, knowing only the nominal values of experimentally measured or computed quantities is insufficient for applications, particularly since the respective experimental and computed nominal values seldom coincide. In the author’s view, the objective of predictive modeling is to extract “best estimate” values for model parameters and predicted results, together with “best estimate” uncertainties for these parameters and results. To achieve this goal, predictive modeling combines imprecisely known experimental and computational data, which calls for reasoning on the basis of incomplete, error-rich, and occasionally discrepant information. The customary methods used for data assimilation combine experimental and computational information by minimizing an a priori, user-chosen, “cost functional” (usually a quadratic functional that represents the weighted errors between measured and computed responses). In contrast to these user-influenced methods, the BERRU (Best Estimate Results with Reduced Uncertainties) Predictive Modeling methodology developed by the author relies on the thermodynamics-based maximum entropy principle to eliminate the need for relying on minimizing user-chosen functionals, thus generalizing the “data adjustment” and/or the “4D-VAR” data assimilation procedures used in the geophysical sciences. The BERRU predictive modeling methodology also provides a “model validation metric” which quantifies the consistency (agreement/disagreement) between measurements and computations. This “model validation metric” (or “consistency indicator”) is constructed from parameter covariance matrices, response covariance matrices (measured and computed), and response sensitivities to model parameters. Traditional methods for computing response sensitivities are hampered by the “curse of dimensionality,” which makes them impractical for applications to large-scale systems that involve many imprecisely known parameters. Reducing the computational effort required for precisely calculating the response sensitivities is paramount, and the comprehensive adjoint sensitivity analysis methodology developed by the author shows great promise in this regard, as shown in this book. After discarding inconsistent data (if any) using the consistency indicator, the BERRU predictive modeling methodology provides best-estimate values for predicted parameters and responses along with best-estimate reduced uncertainties (i.e., smaller predicted standard deviations) for the predicted quantities. Applying the BERRU methodology yields optimal, experimentally validated, “best estimate” predictive modeling tools for designing new technologies and facilities, while also improving on existing ones.
Author: Dan Gabriel Cacuci Publisher: Springer ISBN: 366258395X Category : Technology & Engineering Languages : en Pages : 451
Book Description
This book addresses the experimental calibration of best-estimate numerical simulation models. The results of measurements and computations are never exact. Therefore, knowing only the nominal values of experimentally measured or computed quantities is insufficient for applications, particularly since the respective experimental and computed nominal values seldom coincide. In the author’s view, the objective of predictive modeling is to extract “best estimate” values for model parameters and predicted results, together with “best estimate” uncertainties for these parameters and results. To achieve this goal, predictive modeling combines imprecisely known experimental and computational data, which calls for reasoning on the basis of incomplete, error-rich, and occasionally discrepant information. The customary methods used for data assimilation combine experimental and computational information by minimizing an a priori, user-chosen, “cost functional” (usually a quadratic functional that represents the weighted errors between measured and computed responses). In contrast to these user-influenced methods, the BERRU (Best Estimate Results with Reduced Uncertainties) Predictive Modeling methodology developed by the author relies on the thermodynamics-based maximum entropy principle to eliminate the need for relying on minimizing user-chosen functionals, thus generalizing the “data adjustment” and/or the “4D-VAR” data assimilation procedures used in the geophysical sciences. The BERRU predictive modeling methodology also provides a “model validation metric” which quantifies the consistency (agreement/disagreement) between measurements and computations. This “model validation metric” (or “consistency indicator”) is constructed from parameter covariance matrices, response covariance matrices (measured and computed), and response sensitivities to model parameters. Traditional methods for computing response sensitivities are hampered by the “curse of dimensionality,” which makes them impractical for applications to large-scale systems that involve many imprecisely known parameters. Reducing the computational effort required for precisely calculating the response sensitivities is paramount, and the comprehensive adjoint sensitivity analysis methodology developed by the author shows great promise in this regard, as shown in this book. After discarding inconsistent data (if any) using the consistency indicator, the BERRU predictive modeling methodology provides best-estimate values for predicted parameters and responses along with best-estimate reduced uncertainties (i.e., smaller predicted standard deviations) for the predicted quantities. Applying the BERRU methodology yields optimal, experimentally validated, “best estimate” predictive modeling tools for designing new technologies and facilities, while also improving on existing ones.
Author: Dan Gabriel Cacuci Publisher: ISBN: 9781032740560 Category : Mathematics Languages : en Pages : 0
Book Description
Continuing the author's previous work on modeling, this book presents the most recent advances in high-order predictive modeling. The author begins with the mathematical framework of the 2nd-BERRU-PM methodology, an acronym that designates the "second-order best-estimate with reduced uncertainties (2nd-BERRU) predictive modeling (PM)." The 2nd-BERRU-PM methodology is fundamentally anchored in physics-based principles stemming from thermodynamics (maximum entropy principle) and information theory, being formulated in the most inclusive possible phase-space, namely the combined phase-space of computed and measured parameters and responses. The 2nd-BERRU-PM methodology provides second-order output (means and variances) but can incorporate, as input, arbitrarily high-order sensitivities of responses with respect to model parameters, as well as arbitrarily high-order moments of the initial distribution of uncertain model parameters, in order to predict best-estimate mean values for the model responses (i.e., results of interest) and calibrated model parameters, along with reduced predicted variances and covariances for these predicted responses and parameters.
Author: Dan Gabriel Cacuci Publisher: Springer Nature ISBN: 3031227573 Category : Science Languages : en Pages : 379
Book Description
This text describes a comprehensive adjoint sensitivity analysis methodology (C-ASAM), developed by the author, enabling the efficient and exact computation of arbitrarily high-order functional derivatives of model responses to model parameters in large-scale systems. The model’s responses can be either scalar-valued functionals of the model’s parameters and state variables (as customarily encountered, e.g., in optimization problems) or general function-valued responses, which are often of interest but are currently not amenable to efficient sensitivity analysis. The C-ASAM framework is set in linearly increasing Hilbert spaces, each of state-function-dimensionality, as opposed to exponentially increasing parameter-dimensional spaces, thereby breaking the so-called “curse of dimensionality” in sensitivity and uncertainty analysis. The C-ASAM applies to any model; the larger the number of model parameters, the more efficient the C-ASAM becomes for computing arbitrarily high-order response sensitivities. The text includes illustrative paradigm problems which are fully worked-out to enable the thorough understanding of the C-ASAM’s principles and their practical application. The book will be helpful to those working in the fields of sensitivity analysis, uncertainty quantification, model validation, optimization, data assimilation, model calibration, sensor fusion, reduced-order modelling, inverse problems and predictive modelling. It serves as a textbook or as supplementary reading for graduate course on these topics, in academic departments in the natural, biological, and physical sciences and engineering. This Volume Three, the third of three, covers systems that are nonlinear in the state variables, model parameters and associated responses. The selected illustrative paradigm problems share these general characteristics. A separate Volume One covers systems that are linear in the state variables.
Author: Jeffrey Strickland Publisher: Lulu.com ISBN: 1312375442 Category : Business & Economics Languages : en Pages : 490
Book Description
This book is about predictive modeling. Yet, each chapter could easily be handled by an entire volume of its own. So one might think of this as a survey of predictive models, both statistical and machine learning. We define A predictive model as a statistical model or machine learning model used to predict future behavior based on past behavior. In order to use this book, the reader should have a basic understanding of statistics (statistical inference, models, tests, etc.)-this is an advanced book. Every chapter culminates in an example using R. R is a free software environment for statistical computing and graphics. It compiles and runs on a wide variety of UNIX platforms, Windows and MacOS. The book is organized so that statistical models are presented first (hopefully in a logical order), followed by machine learning models, and then applications: uplift modeling and time series. One could use this as a textbook with problem solving in R (there are no "by-hand" exercises).
Author: Max Kuhn Publisher: Springer Science & Business Media ISBN: 1461468493 Category : Medical Languages : en Pages : 595
Book Description
Applied Predictive Modeling covers the overall predictive modeling process, beginning with the crucial steps of data preprocessing, data splitting and foundations of model tuning. The text then provides intuitive explanations of numerous common and modern regression and classification techniques, always with an emphasis on illustrating and solving real data problems. The text illustrates all parts of the modeling process through many hands-on, real-life examples, and every chapter contains extensive R code for each step of the process. This multi-purpose text can be used as an introduction to predictive models and the overall modeling process, a practitioner’s reference handbook, or as a text for advanced undergraduate or graduate level predictive modeling courses. To that end, each chapter contains problem sets to help solidify the covered concepts and uses data available in the book’s R package. This text is intended for a broad audience as both an introduction to predictive models as well as a guide to applying them. Non-mathematical readers will appreciate the intuitive explanations of the techniques while an emphasis on problem-solving with real data across a wide variety of applications will aid practitioners who wish to extend their expertise. Readers should have knowledge of basic statistical ideas, such as correlation and linear regression analysis. While the text is biased against complex equations, a mathematical background is needed for advanced topics.
Author: Alik Ismail-Zadeh Publisher: Cambridge University Press ISBN: 1009190083 Category : Science Languages : en Pages : 369
Book Description
Many contemporary problems within the Earth sciences are complex, and require an interdisciplinary approach. This book provides a comprehensive reference on data assimilation and inverse problems, as well as their applications across a broad range of geophysical disciplines. With contributions from world leading researchers, it covers basic knowledge about geophysical inversions and data assimilation and discusses a range of important research issues and applications in atmospheric and cryospheric sciences, hydrology, geochronology, geodesy, geodynamics, geomagnetism, gravity, near-Earth electron radiation, seismology, and volcanology. Highlighting the importance of research in data assimilation for understanding dynamical processes of the Earth and its space environment and for predictability, it summarizes relevant new advances in data assimilation and inverse problems related to different geophysical fields. Covering both theory and practical applications, it is an ideal reference for researchers and graduate students within the geosciences who are interested in inverse problems, data assimilation, predictability, and numerical methods.
Author: Steven Taylor Publisher: Steven Taylor ISBN: Category : Science Languages : en Pages : 94
Book Description
Applied Predictive Modeling Predictive modeling uses statistics in order to predict outcomes. However, predictive modeling can be applied to future and to any other kind of unknown event, regardless of when it happened. When it comes to the applications of predictive modeling, techniques are used in various fields including algorithmic trading, uplift modeling, archaeology, health care, customer relationship management and many others. This book covers the predictive modeling process with fundamental steps of the process, data preprocessing, data splitting and crucial steps of model tuning and improving model performance. Further, the book will introduce you to the most common classification and regression techniques including logistic regression which is widely used when it comes to the finding the probability of event success or event failure. You will get to know the common predictive modeling techniques as well such as stepwise regression, polynomial regression and ridge regression which will help you when you are dealing with the data that suffers from very common multicollinearity where independent variables are highly correlated. The text then provides fundamental steps to effective predictive modeling. In the second chapter, you will learn how to build your own predictive model with logistic regression and Python. You will find data sets as well as corresponding codes. On of the crucial predictive modeling steps is model tuning, so you will learn some common techniques used in order to improve your model performance. You will get to know how to tune the parameters commonly used to increase the overall predictive power. Predictive modeling comes with a few obstacles and challenges like class imbalance. Imbalanced classes commonly put the accuracy of the model out of business, but you will learn how to properly handle class imbalance which will significantly improve the accuracy of your model. The book is multi-purpose focused on to predictive modeling process and predictive modeling techniques, so it will be of great help for those who are interested in predictive modeling techniques and applications. So, it is the right time to simplify the analysis, boost productivity as well as save time. The book will be your companion on your journey towards highly accurate predictive models. What you will learn in Applied Predictive Modeling: Most common predictive modeling techniques Types of regression models The overall predictive modeling process Fundamental steps to effective and highly accurate predictive modeling How to build predictive model with logistic regression with code listings How to build predictive model using Python How to enhance your model performance Parameters for increasing the overall predictive power How to handle class imbalance Common causes of poor model performance Get this book now and learn more about Applied Predictive Modeling!
Author: Dan Gabriel Cacuci Publisher: Springer Nature ISBN: 303119635X Category : Science Languages : en Pages : 474
Book Description
This text describes a comprehensive adjoint sensitivity analysis methodology (nth-CASAM), developed by the author, which enablesthe efficient and exact computation of arbitrarily high-order functional derivatives of model responses to model parameters in large-scale systems. The nth-CASAM framework is set in linearly increasing Hilbert spaces, each of state-function-dimensionality, as opposed to exponentially increasing parameter-dimensional spaces, thereby overcoming the so-called “curse of dimensionality” in sensitivity and uncertainty analysis. The nth-CASAM is applicable to any model; the larger the number of model parameters, the more efficient the nth-CASAM becomes for computing arbitrarily high-order response sensitivities. The book will be helpful to those working in the fields of sensitivity analysis, uncertainty quantification, model validation, optimization, data assimilation, model calibration, sensor fusion, reduced-order modelling, inverse problems and predictive modelling. This Volume Two, the second of three, presents the large-scale application of the nth-CASAM to perform a representative fourth-order sensitivity analysis of the Polyethylene-Reflected Plutonium benchmark described in the Nuclear Energy Agency (NEA) International Criticality Safety Benchmark Evaluation Project (ICSBEP) Handbook. This benchmark is modeled mathematically by the Boltzmann particle transport equation, involving 21,976 imprecisely-known parameters, the numerical solution of which requires representative large-scale computations. The sensitivity analysis presented in this volume is the most comprehensive ever performed in the field of reactor physics and the results presented in this book prove, perhaps counter-intuitively, that many of the 4th-order sensitivities are much larger than the corresponding 3rd-order ones, which are, in turn, much larger than the 2nd-order ones, all of which are much larger than the 1st-order sensitivities. Currently, the nth-CASAM is the only known methodology which enables such large-scale computations of exactly obtained expressions of arbitrarily-high-order response sensitivities.
Author: Max Kuhn Publisher: CRC Press ISBN: 1351609475 Category : Business & Economics Languages : en Pages : 298
Book Description
The process of developing predictive models includes many stages. Most resources focus on the modeling algorithms but neglect other critical aspects of the modeling process. This book describes techniques for finding the best representations of predictors for modeling and for nding the best subset of predictors for improving model performance. A variety of example data sets are used to illustrate the techniques along with R programs for reproducing the results.
Author: Max Kuhn Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
This is a book on data analysis with a specific focus on the practice of predictive modeling, which is associated with machine learning, pattern recognition and data mining.The practive of predictive modeling defines the process of developing a model in a way that we can understand and quatify the model's prediction accuracy on future.
Author: Dan Gabriel Cacuci
Author: Dan Gabriel Cacuci
Author: Dan Gabriel Cacuci
Author: Dan Gabriel Cacuci
Author: Jeffrey Strickland
Author: Max Kuhn
Author: Alik Ismail-Zadeh
Author: Steven Taylor
Author: Dan Gabriel Cacuci
Author: Max Kuhn
Author: Max Kuhn