A systems-based approach to multiscale computation: Equation-free detection of coarse-grained bifurcations

摘要

We discuss certain basic features of the equation-free (EF) approach to modeling and computation for complex/multiscale systems.We focus on links between the equation-free approach and tools from systems and control theory (design of experiments,data analysis,estimation,identification and feedback).As our illustrative example,we choose a specific numerical task (the detection of stability boundaries in parameter space) for stochastic models of two simplified heterogeneous catalytic reaction mechanisms.In the equation-free framework the stochastic simulator is treated as an experiment (albeit a computational one).Short bursts of fine scale simulation (short computational experiments) are designed,executed,and their outputs processed and fed back to the process,in integrated protocols aimed at performing the particular coarse-grained task (the detection of a macroscopic instability).Two distinct approaches are presented;one is a direct translation of our previous protocol for adaptive detection of instabilities in laboratory experiments [Rico-Martinez,R.,Krisher,K.,Flatgen,G.,Anderson,J.S.,& Kevrekidis,I.G.(2003).Adaptive detection of instabilities: An experimental feasibility study.Physica D,176,1-18];the second approach is motivated from numerical bifurcation algorithms for critical point detection.A comparison of the two approaches brings forth a key feature of equation-free computation: computational experiments can be easily initialized at will,in contrast to laboratory ones.