Coping with Complexity: Model Reduction and Data Analysis

Front Matter....Pages i-xii
Averaging of Fast-Slow Systems....Pages 1-7
The Use of Global Sensitivity Methods for the Analysis, Evaluation and Improvement of Complex Modelling Systems....Pages 9-36
Optimisation and Linear Control of Large Scale Nonlinear Systems: A Review and a Suite of Model Reduction-Based Techniques....Pages 37-61
Universal Algorithms, Mathematics of Semirings and Parallel Computations....Pages 63-89
Scaling Invariant Interpolation for Singularly Perturbed Vector Fields (SPVF)....Pages 91-111
Think Globally, Move Locally: Coarse Graining of Effective Free Energy Surfaces....Pages 113-131
Extracting Functional Dependence from Sparse Data Using Dimensionality Reduction: Application to Potential Energy Surface Construction....Pages 133-149
A Multilevel Algorithm to Compute Steady States of Lattice Boltzmann Models....Pages 151-167
Time Step Expansions and the Invariant Manifold Approach to Lattice Boltzmann Models....Pages 169-205
The Shock Wave Problem Revisited: The Navier–Stokes Equations and Brenner’s Two Velocity Hydrodynamics....Pages 207-229
Adaptive Simplification of Complex Systems: A Review of the Relaxation-Redistribution Approach....Pages 231-240
Geometric Criteria for Model Reduction in Chemical Kinetics via Optimization of Trajectories....Pages 241-252
Computing Realizations of Reaction Kinetic Networks with Given Properties....Pages 253-267
A Drift-Filtered Approach to Diffusion Estimation for Multiscale Processes....Pages 269-286
Model Reduction of a Higher-Order KdV Equation for Shallow Water Waves....Pages 287-298
Coarse Collective Dynamics of Animal Groups....Pages 299-309
Self-Simplification in Darwin’s Systems....Pages 311-344
Back Matter....Pages 345-348