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Coping with Complexity: Model Reduction and Data Analysis

  • Conference proceedings
  • © 2011

Overview

Editors:
  1. Alexander N. Gorban

    1. Dept. Mathematics, University of Leicester, Leicester, United Kingdom

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  2. Dirk Roose

    1. Dept. Computer Science, Katholieke Universiteit Leuven, Leuven, Belgium

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  • Highly interdisciplinary and helps to circumvent the “language barriers” between different disciplines.
  • Gives the reader an view on the state-of-the-art in both theoretical and practical issues in model reduction and data analysis of complex and multiscale mathematical models.

Part of the book series: Lecture Notes in Computational Science and Engineering (LNCSE, volume 75)

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Table of contents (17 papers)

  1. Front Matter

    Pages i-xii
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  2. Averaging of Fast-Slow Systems

    • Marshall Slemrod
    Pages 1-7

  3. The Use of Global Sensitivity Methods for the Analysis, Evaluation and Improvement of Complex Modelling Systems

    • Alison S. Tomlin, Tilo Ziehn
    Pages 9-36

  4. Optimisation and Linear Control of Large Scale Nonlinear Systems: A Review and a Suite of Model Reduction-Based Techniques

    • Constantinos Theodoropoulos
    Pages 37-61

  5. Universal Algorithms, Mathematics of Semirings and Parallel Computations

    • Grigory L. Litvinov, Victor P. Maslov, Anatoly Ya. Rodionov, Andrei N. Sobolevski
    Pages 63-89

  6. Scaling Invariant Interpolation for Singularly Perturbed Vector Fields (SPVF)

    • Viatcheslav Bykov, Vladimir Gol’dshtein, Ulrich Maas
    Pages 91-111

  7. Think Globally, Move Locally: Coarse Graining of Effective Free Energy Surfaces

    • Payel Das, Thomas A. Frewen, Ioannis G. Kevrekidis, Cecilia Clementi
    Pages 113-131

  8. Extracting Functional Dependence from Sparse Data Using Dimensionality Reduction: Application to Potential Energy Surface Construction

    • Sergei Manzhos, Koichi Yamashita, Tucker Carrington
    Pages 133-149

  9. A Multilevel Algorithm to Compute Steady States of Lattice Boltzmann Models

    • Giovanni Samaey, Christophe Vandekerckhove, Wim Vanroose
    Pages 151-167

  10. Time Step Expansions and the Invariant Manifold Approach to Lattice Boltzmann Models

    • David J. Packwood, Jeremy Levesley, Alexander N. Gorban
    Pages 169-205

  11. The Shock Wave Problem Revisited: The Navier–Stokes Equations and Brenner’s Two Velocity Hydrodynamics

    • Francisco J. Uribe
    Pages 207-229

  12. Adaptive Simplification of Complex Systems: A Review of the Relaxation-Redistribution Approach

    • Eliodoro Chiavazzo, Ilya Karlin
    Pages 231-240

  13. Geometric Criteria for Model Reduction in Chemical Kinetics via Optimization of Trajectories

    • Dirk Lebiedz, Volkmar Reinhardt, Jochen Siehr, Jonas Unger
    Pages 241-252

  14. Computing Realizations of Reaction Kinetic Networks with Given Properties

    • Gábor Szederkényi, Katalin M. Hangos, Dávid Csercsik
    Pages 253-267

  15. A Drift-Filtered Approach to Diffusion Estimation for Multiscale Processes

    • Yves Frederix, Dirk Roose
    Pages 269-286

  16. Model Reduction of a Higher-Order KdV Equation for Shallow Water Waves

    • Tassos Bountis, Ko van der Weele, Giorgos Kanellopoulos, Kostis Andriopoulos
    Pages 287-298

  17. Coarse Collective Dynamics of Animal Groups

    • Thomas A. Frewen, Iain D. Couzin, Allison Kolpas, Jeff Moehlis, Ronald Coifman, Ioannis G. Kevrekidis
    Pages 299-309

  18. Self-Simplification in Darwin’s Systems

    • Alexander N. Gorban
    Pages 311-344

  19. Back Matter

    Pages 345-348
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Keywords

About this book

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.

Editors and Affiliations

  • Dept. Mathematics, University of Leicester, Leicester, United Kingdom

    Alexander N. Gorban

  • Dept. Computer Science, Katholieke Universiteit Leuven, Leuven, Belgium

    Dirk Roose

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