Model Reduction and Approximation

Model Reduction and Approximation

Author: Peter Benner

Publisher: SIAM

Published: 2017-07-06

Total Pages: 421

ISBN-13: 1611974828

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Many physical, chemical, biomedical, and technical processes can be described by partial differential equations or dynamical systems. In spite of increasing computational capacities, many problems are of such high complexity that they are solvable only with severe simplifications, and the design of efficient numerical schemes remains a central research challenge. This book presents a tutorial introduction to recent developments in mathematical methods for model reduction and approximation of complex systems. Model Reduction and Approximation: Theory and Algorithms contains three parts that cover (I) sampling-based methods, such as the reduced basis method and proper orthogonal decomposition, (II) approximation of high-dimensional problems by low-rank tensor techniques, and (III) system-theoretic methods, such as balanced truncation, interpolatory methods, and the Loewner framework. It is tutorial in nature, giving an accessible introduction to state-of-the-art model reduction and approximation methods. It also covers a wide range of methods drawn from typically distinct communities (sampling based, tensor based, system-theoretic).?? This book is intended for researchers interested in model reduction and approximation, particularly graduate students and young researchers.


Structure and Approximation in Physical Theories

Structure and Approximation in Physical Theories

Author: A. Hartkamper

Publisher: Springer Science & Business Media

Published: 2013-11-11

Total Pages: 254

ISBN-13: 1468441094

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The present volume contains 14 contributions presented at a colloquium on "Structure and Approximation in Physical Theories" held at Osnabruck in June 1980. The articles are presented in the revised form written after the colloquium and hence also take account of the results of the discussion at the colloquium. It is a striking feature that the problem of approximation in physical theories has only recently found some attention in the philosophy of science, although the working physicist is con stantly confronted with those questions. No interesting theory of exact science exactly fits its experimental data; almost every relation between different theories is an approximate one. There fore an adequate reconstruction of physical theories must take into account and conceptualize the moment of approximation. The majority of the articles in this book is centered around this subject. There are at least two elaborate, 'structuralistic' approaches to the formalization of physical theories in which the aspect of approximation has been incorporated: the approach due to P. Suppes, J. Sneed, W. Stegmuller ("S-approach") and the approach of G. Lud wig and his co-workers ("L-approach"). The articles in this book correspondingly fall into three classes: presentation, elaboration and critique of the L-approach [Hartkamper/Schmidt, Ludwig, Neumann, Werner, Schmidt, Mayr, Kamiah, Majer, Grafe] or of the S-approach [Moulines, Balzer, Cooke], and articles referring to both approaches or concerned with related matters [Scheibe, Pfarr, Castrigiano]. Of course, this is only a rough classification and each article must be appraised in its own right.


Encyclopedia of Evolutionary Biology

Encyclopedia of Evolutionary Biology

Author:

Publisher: Academic Press

Published: 2016-04-14

Total Pages: 2138

ISBN-13: 0128004266

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Encyclopedia of Evolutionary Biology, Four Volume Set is the definitive go-to reference in the field of evolutionary biology. It provides a fully comprehensive review of the field in an easy to search structure. Under the collective leadership of fifteen distinguished section editors, it is comprised of articles written by leading experts in the field, providing a full review of the current status of each topic. The articles are up-to-date and fully illustrated with in-text references that allow readers to easily access primary literature. While all entries are authoritative and valuable to those with advanced understanding of evolutionary biology, they are also intended to be accessible to both advanced undergraduate and graduate students. Broad topics include the history of evolutionary biology, population genetics, quantitative genetics; speciation, life history evolution, evolution of sex and mating systems, evolutionary biogeography, evolutionary developmental biology, molecular and genome evolution, coevolution, phylogenetic methods, microbial evolution, diversification of plants and fungi, diversification of animals, and applied evolution. Presents fully comprehensive content, allowing easy access to fundamental information and links to primary research Contains concise articles by leading experts in the field that ensures current coverage of each topic Provides ancillary learning tools like tables, illustrations, and multimedia features to assist with the comprehension process


Approximation Methods for High Dimensional Simulation Results - Parameter Sensitivity Analysis and Propagation of Variations for Process Chains

Approximation Methods for High Dimensional Simulation Results - Parameter Sensitivity Analysis and Propagation of Variations for Process Chains

Author: Daniela Steffes-lai

Publisher: Logos Verlag Berlin GmbH

Published: 2014

Total Pages: 232

ISBN-13: 3832536965

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This work addresses the analysis of a sequential chain of processing steps, which is particularly important for the manufacture of robust product components. In each processing step, the material properties may have changed and distributions of related characteristics, for example, strains, may become inhomogeneous. For this reason, the history of the process including design-parameter uncertainties becomes relevant for subsequent processing steps. Therefore, we have developed a methodology, called PRO-CHAIN, which enables an efficient analysis, quantification, and propagation of uncertainties for complex process chains locally on the entire mesh. This innovative methodology has the objective to improve the overall forecast quality, specifically, in local regions of interest, while minimizing the computational effort of subsequent analysis steps. We have demonstrated the benefits and efficiency of the methodology proposed by means of real applications from the automotive industry.


The Philosophy Behind Physics

The Philosophy Behind Physics

Author: Thomas A. Brody

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 361

ISBN-13: 3642789781

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Thomas Brody had one of the most powerful and wide-ranging intellects of his generation. Although primarily a physicist who worked on statistical prob lems in nuclear physics, on probability theory and on computational physics he had an extensive knowledge of the philosophy of science and of philosophy, and was fluent in many languages. He is well-known among physicists for the Brody-Moshinsky transformation but his extensive work on probability and on the philosophy of science remained almost unknown. This was because the originality of his ideas entailed many lengthy battles with uncomprehending referees, and he frequently published in Mexican journals of limited circula tion. In addition, his strongly critical spirit inhibited his willingness to publish his ideas. He was always most concerned by the very unsatisfactory situation in the philosophy of physics, that is largely due to the generally poor knowledge that physicists and philosophers have of each other's disciplines. Philosophers of science write at length about physics without any detailed first-hand knowl edge of how research is actually carried out. Physicists, for their part, often implicitly assume naive or erroneous philosophical ideas, and this often hinders their scientific work, besides spreading further confusion if they try to give an account of what they are doing.