Modern science is, to a large extent, a model-building activity. But how are models contructed? How are they related to theories and data? How do they explain complex scientific phenomena, and which role do computer simulations play here? These questions have kept philosophers of science busy for many years, and much work has been done to identify modeling as the central activity of theoretical science. At the same time, these questions have been addressed by methodologically-minded scientists, albeit from a different point of view. While philosophers typically have an eye on general aspects of scientific modeling, scientists typically take their own science as the starting point and are often more concerned with specific methodological problems. There is, however, also much common ground in middle, where philosophers and scientists can engage in a productive dialogue, as the present volume demonstrates. To do so, the editors of this volume have invited eight leading scientists from cosmology, climate science, social science, chemical engeneering and neuroscience to reflect upon their modeling work, and eight philosophers of science to provide a commentary.

Despite the continued rapid advance in computing speed and memory the increase in the complexity of models used by engineers persists in outpacing them. Even where there is access to the latest hardware, simulations are often extremely computationally intensive and time-consuming when full-blown models are under consideration. The need to reduce the computational cost involved when dealing with high-order/many-degree-of-freedom models can be offset by adroit computation. In this light, model-reduction methods have become a major goal of simulation and modeling research. Model reduction can also ameliorate problems in the correlation of widely used finite-element analyses and test analysis models produced by excessive system complexity. Model Order Reduction Techniques explains and compares such methods focusing mainly on recent work in dynamic condensation techniques: - Compares the effectiveness of static, exact, dynamic, SEREP and iterative-dynamic condensation techniques in producing valid reduced-order models; - Shows how frequency shifting and the number of degrees of freedom affect the desirability and accuracy of using dynamic condensation; - Answers the challenges involved in dealing with undamped and non-classically damped models; - Requires little more than first-engineering-degree mathematics and highlights important points with instructive examples. Academics working in research on structural dynamics, MEMS, vibration, finite elements and other computational methods in mechanical, aerospace and structural engineering will find Model Order Reduction Techniques of great interest while it is also an excellent resource for researchers working on commercial finite-element-related software such as ANSYS and Nastran.

This volume contains the extended version of selected talks given at the international research workshop "Coping with Complexity: Model Reduction and Data Analysis", Ambleside, UK, August 31 – September 4, 2009. The book is deliberately broad in scope and aims at promoting new ideas and methodological perspectives. The topics of the chapters range from theoretical analysis of complex and multiscale mathematical models to applications in e.g., fluid dynamics and chemical kinetics.

Simulation based on mathematical models plays a major role in computer aided design of integrated circuits (ICs). Decreasing structure sizes, increasing packing densities and driving frequencies require the use of refined mathematical models, and to take into account secondary, parasitic effects. This leads to very high dimensional problems which nowadays require simulation times too large for the short time-to-market demands in industry. Modern Model Order Reduction (MOR) techniques present a way out of this dilemma in providing surrogate models which keep the main characteristics of the device while requiring a significantly lower simulation time than the full model. With Model Reduction for Circuit Simulation we survey the state of the art in the challenging research field of MOR for ICs, and also address its future research directions. Special emphasis is taken on aspects stemming from miniturisations to the nano scale. Contributions cover complexity reduction using e.g., balanced truncation, Krylov-techniques or POD approaches. For semiconductor applications a focus is on generalising current techniques to differential-algebraic equations, on including design parameters, on preserving stability, and on including nonlinearity by means of piecewise linearisations along solution trajectories (TPWL) and interpolation techniques for nonlinear parts. Furthermore the influence of interconnects and power grids on the physical properties of the device is considered, and also top-down system design approaches in which detailed block descriptions are combined with behavioral models. Further topics consider MOR and the combination of approaches from optimisation and statistics, and the inclusion of PDE models with emphasis on MOR for the resulting partial differential algebraic systems. The methods which currently are being developed have also relevance in other application areas such as mechanical multibody systems, and systems arising in chemistry and to biology. The current number of books in the area of MOR for ICs is very limited, so that this volume helps to fill a gap in providing the state of the art material, and to stimulate further research in this area of MOR. Model Reduction for Circuit Simulation also reflects and documents the vivid interaction between three active research projects in this area, namely the EU-Marie Curie Action ToK project O-MOORE-NICE (members in Belgium, The Netherlands and Germany), the EU-Marie Curie Action RTN-project COMSON (members in The Netherlands, Italy, Germany, and Romania), and the German federal project System reduction in nano-electronics (SyreNe).

The idea for this book originated during the workshop “Model order reduction, coupled problems and optimization” held at the Lorentz Center in Leiden from S- tember 19–23, 2005. During one of the discussion sessions, it became clear that a book describing the state of the art in model order reduction, starting from the very basics and containing an overview of all relevant techniques, would be of great use for students, young researchers starting in the ?eld, and experienced researchers. The observation that most of the theory on model order reduction is scattered over many good papers, making it dif?cult to ?nd a good starting point, was supported by most of the participants. Moreover, most of the speakers at the workshop were willing to contribute to the book that is now in front of you. The goal of this book, as de?ned during the discussion sessions at the workshop, is three-fold: ?rst, it should describe the basics of model order reduction. Second, both general and more specialized model order reduction techniques for linear and nonlinear systems should be covered, including the use of several related numerical techniques. Third, the use of model order reduction techniques in practical appli- tions and current research aspects should be discussed. We have organized the book according to these goals. In Part I, the rationale behind model order reduction is explained, and an overview of the most common methods is described.

The book contains the Proceedings of the 2010 Conference of the Italian Systems Society. Papers deal with the interdisciplinary study of processes of changing related to a wide variety of specific disciplinary aspects. Classical attempts to deal with them, based on generalising approaches used to study the movement of bodies and environmental influence, have included ineffective reductionistic simplifications. Indeed changing also relates, for instance, to processes of acquisition and varying properties such as for software; growing and aging biological systems; learning/cognitive systems; and socio-economic systems growing and developing through innovations. Some approaches to modelling such processes are based on considering changes in structure, e.g., phase-transitions. Other approaches are based on considering (1) periodic changes in structure as for processes of self-organisation; (2) non-periodic but coherent changes in structure, as for processes of emergence; (3) the quantum level of description. Papers in the book study the problem considering its transdisciplinary nature, i.e., systemic properties studied per se and not within specific disciplinary contexts. The aim of these studies is to outline a transdisciplinary theory of change in systemic properties. Such a theory should have simultaneous, corresponding and eventually hierarchical disciplinary aspects as expected for a general theory of emergence. Within this transdisciplinary context, specific disciplinary research activities and results are assumed to be mutually represented as within a philosophical and conceptual framework based on the theoretical centrality of the observer and conceptual non-separability of context and observer, related to logically open systems and Quantum Entanglement. Contributions deal with such issues in interdisciplinary ways considering theoretical aspects and applications from Physics, Cognitive Science, Biology, Artificial Intelligence, Economics, Architecture, Philosophy, Music and Social Systems.