TY - JOUR

T1 - A systems-based approach to multiscale computation

T2 - Equation-free detection of coarse-grained bifurcations

AU - Siettos, C. I.

AU - Rico-Martinez, R.

AU - Kevrekidis, I. G.

N1 - Funding Information:
The work of IGK was partially supported through AFOSR, DARPA, an NSF/ITR grant and a Guggenheim Fellowship. CS acknowledges partial support by the European Social Fund and National Resources, (EPEAEKII), Pythagoras.

PY - 2006/9/12

Y1 - 2006/9/12

N2 - 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.

AB - 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.

KW - Bifurcation

KW - Equation-free

KW - Multiscale

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U2 - 10.1016/j.compchemeng.2006.05.019

DO - 10.1016/j.compchemeng.2006.05.019

M3 - Article

AN - SCOPUS:33747887361

VL - 30

SP - 1632

EP - 1642

JO - Computers and Chemical Engineering

JF - Computers and Chemical Engineering

SN - 0098-1354

IS - 10-12

ER -