Coping with Complexity: Model Reduction and Data Analysis

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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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.

• asymptotics
• dimensionality reduction
• invariant manifolds
• kinetics
• model reduction
• singular perturbation

• 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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